Answer:
The test is a two -tailed test
Step-by-step explanation:
From the question we are told that
The sample size is n = 31
The sample mean is [tex]\= x =11[/tex]
The sample standard deviation is [tex]\sigma = 3[/tex]
The null hypothesis is [tex]H_o: \mu \le 10[/tex]
The alternative hypothesis is [tex]H_1 : \mu > 10[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 11 - 10 }{ \frac{3}{\sqrt{ 31} } }[/tex]
[tex]t = 1.85[/tex]
The p- value is mathematically represented as
[tex]p-value = p( t > 1.856) = 0.0317[/tex]
Looking at the value of [tex]p-value \ and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] hence we reject the null hypothesis
Given the that the p value is less than 0.05 it mean the this is a two-tailed test
A boutique wants to make at least $127 profit from purses this week. The boutique earns $7 profit from each purse. How many purses must be sold?
Answer:
19 purses
Step-by-step explanation:
Set up an inequality where x represents the number of purses:
127 [tex]\geq[/tex] 7x
Solve for x by dividing each side by 7:
18.14 [tex]\geq[/tex] x
Round up to 19 because purses have to be whole
So, 19 purses have to be sold.
Dada la recta L: 3x - 2y + 1 = 0, ¿cual es la pendiente de la recta L1?
Answer:
La pendiente de la recta L es [tex]\frac{3}{2}[/tex].
Step-by-step explanation:
La recta está presentada en su forma implícita, es decir, que está bajo la forma:
[tex]f(x,y) = 0[/tex]
Para determinar la pendiente de la recta, se debe transformarla a su forma explícita, cuya fórmula es:
[tex]y = m \cdot x + b[/tex]
Donde:
[tex]x[/tex] - Variable independiente, adimensional.
[tex]y[/tex] - Variable dependiente, adimensional.
[tex]m[/tex] - Pendiente, adimensional.
[tex]b[/tex] - Intercepto, adimensional.
Entonces:
[tex]3\cdot x - 2\cdot y + 1 = 0[/tex]
[tex]2\cdot y = 3\cdot x +1[/tex]
[tex]y = \frac{3}{2}\cdot x + \frac{1}{2}[/tex]
Por simple inspección, se determina que la pendiente de la recta L es [tex]\frac{3}{2}[/tex].
A certain dataset of systolic blood pressure measurements has a mean of 80 and a standard deviation of 3. Assuming the distribution is bell-shaped and we randomly select a measurement:
a) What percentage of measurements are between 71 and 89?
b) What is the probability a person's blood systolic pressure measures more than 89?
c) What is the probability a person's blood systolic pressure being at most 75?
d) We should expect 15% of patients have a blood pressure below what measurement?
e) Would it be unusual for 3 patients to have a mean blood pressure measurement of more than 84? Explain.
Answer:
Explained below.
Step-by-step explanation:
Let X = systolic blood pressure measurements.
It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].
(a)
Compute the percentage of measurements that are between 71 and 89 as follows:
[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]
[tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of measurements that are between 71 and 89 is 99.73%.
(b)
Compute the probability that a person's blood systolic pressure measures more than 89 as follows:
[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.
(c)
Compute the probability that a person's blood systolic pressure being at most 75 as follows:
Apply continuity correction:
[tex]P(X\leq 75)=P(X<75-0.5)[/tex]
[tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]
Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.
(d)
Let x be the blood pressure required.
Then,
P (X < x) = 0.15
⇒ P (Z < z) = 0.15
⇒ z = -1.04
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]
Thus, the 15% of patients are expected to have a blood pressure below 76.9.
(e)
A z-score more than 2 or less than -2 are considered as unusual.
Compute the z score for [tex]\bar x[/tex] as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]
The z-score for the mean blood pressure measurement of 3 patients is more than 2.
Thus, it would be unusual.
Can someone help? This hard
Answer:
The expression = [tex] \frac{40}{y - 16} [/tex]
Value of the expression = 4 (when y is 20)
Step-by-step explanation:
Quotient simply means the result you get when you divide two numbers. Thus, dividend (the numerator) ÷ divisor (the denominator) = quotient.
From the information given to us here,
the dividend = 40
the divisor = y - 16
The quotient = [tex] \frac{40}{y - 16} [/tex]
There, the expression would be [tex] \frac{40}{y - 16} [/tex]
Find the value of the expression when y = 20.
Plug in 20 for y in the expression and evaluate.
[tex] \frac{40}{y - 16} [/tex]
[tex] = \frac{40}{20 - 16} [/tex]
[tex] = \frac{40}{4} = 10 [/tex]
The value of the expression, when y is 20, is 4.
I need help please help me
Answer: 72576m7
Step-by-step explanation:
2m x 8m x 6m x 9m x 7m x 6m x 2m
All together equals my answer 72576m7
Hope this helps!
Mathematical induction is:
Answer:
The third option.
Step-by-step explanation:
Mathematical induction is a 2 step mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number.
Step 1 (Base step) - It proves that a statement is true for the initial value.
Step 2 (Inductive step) - It proves that if the statement is true for the nth iteration (or number n), then it is also true for (n + 1)th iteration (or number n + 1)
Hope this helps.
Please mark Brainliest.
Answer:
A method of improving statments
Step-by-step explanation:
"Mathematical Induction is a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number."
Customers arrive at a rate of 24 people per hour to a bank. Assume that the number of customers arriving can be described using the Poisson distribution. What is the probability that at most 30 customers arrive in the next hour
Answer:
0.90415
Step-by-step explanation:
Given the following :
Arrival rate = mean(μ) = 24
Probability that at most 30 customers arrive in the next hour:
The poisson distribution formula :
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
P(x ⩽ 30) = p(0) + p(1) + p(2) +.... + p(30)
Using the online poisson probability distribution calculator :
P(x ⩽ 30, 24) = 0.90415
Therefore there is about 90.4% probability that at most 30 customers will arrive in the next hour.
A study was conducted to assess the effects that occur when children are exposed to cocaine before birth. Children were tested at age 4 for object assembly skill, which was described as a task requiring visual spatial skills related to mathematical competence. The 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0 Use a 0.05 significance level to test the claim that prenatal cocaine exposure is associated with lower scores of four year old children on the test of object assembly.
What are null and alternative hypothesis? What is test statistics?
Answer:
We conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.
Step-by-step explanation:
We are given that the 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0.
Let [tex]\mu_1[/tex] = population mean score for children born to cocaine users.
[tex]\mu_2[/tex] = population mean score for children not exposed to cocaine.
So, Null Hypothesis, : = 490 {means that the prenatal cocaine exposure is not associated with lower scores of four-year-old children on the test of object assembly}
Alternate Hypothesis, : 490 {means that the prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean score of children born to cocaine users = 7.3
[tex]\bar X_2[/tex] = sample mean score of children not exposed to cocaine = 8.2
[tex]s_1[/tex] = sample standard deviation for children born to cocaine users = 3
[tex]s_2[/tex] = sample standard deviation for children not exposed to cocaine = 3
[tex]n_1[/tex] = sample of children born to cocaine users = 190
[tex]n_2[/tex] = sample of children not exposed to cocaine = 186
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(190-1)\times 3^{2}+(186-1)\times 3^{2} }{190+186-2} }[/tex] = 3
So, the test statistics = ~
= -2.908
The value of t-test statistics is -2.908.
Now, at a 0.05 level of significance, the t table gives a critical value of -1.645 at 374 degrees of freedom for the left-tailed test.
Since the value of our test statistics is less than the critical value of t as -2.908 < -1.645, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.
In the null hypothesis, a test always forecasts no effect, while the alternate theory states the research expectation impact, and calculation as follows:
Null and alternative hypothesis:Calculating the pooled estimator of [tex]\sigma^2[/tex], denoted by [tex]S^2_p[/tex], is defined by
[tex]\to \bold{S^2_p= \frac{(n_1 - 1) S^2_1+ (n_2 - 1)S^2_2}{n_1 + n_2 - 2}}[/tex]
Null hypothesis:
[tex]\to H_0 : \mu_1 - \mu_2 = \Delta_0\\[/tex]
Test statistic:
[tex]\to T_0=\frac{\bar{X_1}- \bar{X_2} -\Delta_0}{S_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \\\\[/tex]
Alternative Hypothesis:
[tex]H_1 : \mu_1 -\mu_2 \neq \Delta_0\\\\ H_1 : \mu_1 -\mu_2 > \Delta_0\\\\H_1 : \mu_1 -\mu_2 < \Delta_0\\\\[/tex]
Rejection Criterion
[tex]t_0 > t_{\frac{\alpha}{2} , n_1+n_2 -2}\ \ \ or\ \ \ t_0 < - t_{\frac{\alpha}{2} , n_1+n_2 -2} \\\\t_o > t_{\alpha , n_1+n_2 -2} \\\\t_o > -t_{\alpha , n_1+n_2 -2}[/tex]
Given value:
[tex]\to S_p=9\\\\\to \Delta_0=0\\\\\to t_0=-\frac{0.9}{3(\sqrt{(\frac{1}{190}+\frac{1}{186})})}=-2.9\\\\\to t_{0.05,374}=1.645\\\\[/tex]
here
[tex]\to t_0 < -t_{0.05,374}[/tex]
hence rejecting the [tex]H_0[/tex]
Since there should be enough evidence that prenatal cocaine exposure is linked to inferior item assembly scores in 4-year-olds.
Find out more about the alternative hypothesis here:
brainly.com/question/18831983
What is x? Round to the nearest tenth
Answer:
x = 38.7
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan x = 8/10
taking the inverse tan of each side
x = tan ^-1 (8/10)
x=38.65980825
To the nearest tenth
x = 38.7
(1-Cota)^2
+(tana-1)^2=4cosec2a(cosec2a-1)
Answer:
Step-by-step explanation:
(1-CotA)² + (tanA-1)² = 4csc2A(csc2A-1)
To prove this equation we will take the expression given in left hand side and will convert it into the expression given in right hand side of the equation.
L.H.S. = (1-CotA)² + (tanA-1)²
= 1 + Cot²A - 2CotA + 1 + tan²A - 2tanA
= cosec²A - 2CotA + Sec²A - 2tanA
[Since, (1 + Cot²A = cosec²A) and (1 + tan²A = Sec²A)]
= (cosec²A + Sec²A) - 2(CotA + tanA)
= [tex](\frac{1}{\text{SinA}})^{2}+(\frac{1}{CosA} )^{2}-2\text{(tanA}+\frac{1}{\text{tanA}})}[/tex]
= [tex]\frac{1}{(\text{SinA.CosA})^2}-2(\frac{tan^2A+1}{tanA} )[/tex]
= [tex]\frac{4}{\text{(Sin2A})^{2}}-4(\frac{1}{\text{Sin2A}} )[/tex]
[Since 2SinA.CosA = Sin2A and [tex]\frac{2(\text{tanA})}{1+\text{tan}^{2}A}=\text{Sin2A}[/tex]]
= 4Cosec²2A - 4Cosec2A
= 4Cosec2A(Cosec2A - 1)
= R.H.S. (Right hand side)
Hence the equation is proved.
The Rogers family drove 220 miles in 5.5 hours. How many miles would they drive at this same rate in 4 hours? A. 88 mi B. 147 mi C. 160 mi D. 179 mi Please show ALL work! <3
Answer:
160 miles
Step-by-step explanation:
We can use a ratio to solve
220 miles x miles
--------------- = ----------------------
5.5 hours 4 hours
Using cross products
220 *4 = 5.5x
880 = 5.5x
Divide each side by 5.5
880/5.5 = x
160 miles
Answer:
[tex]\large \boxed{\mathrm{C. \ 160 \ miles}}[/tex]
Step-by-step explanation:
We can solve this problem by ratios.
Let x be the missing value.
[tex]\displaystyle \frac{220}{5.5} =\frac{x}{4}[/tex]
Cross multiply.
[tex]5.5 \times x = 220 \times 4[/tex]
[tex]5.5x=880[/tex]
Divide both sides by 5.5.
[tex]\displaystyle \frac{5.5x}{5.5} =\frac{880}{5.5}[/tex]
[tex]x=160[/tex]
What is the distance between y=2x+4 and y=2x-1?
Answer:
Y=2(1)+4
Y=2+4
Y=6
Step-by-step explanation:
Please follow me
Please help!! find the value of the expression
Answer:
7
Step-by-step explanation:
First plug in the variable amounts so the expression now looks like this:
(3 × 4 - 12) + 1/2(4 × 6 - 10)
Now, start by solving the multiplication parts first, so it now looks like this:
(12 - 12) + 1/2(24 - 10)
Now, apply the rules of order of operation, so start by solving what's in parenthesis. It should now look like this: (0) + 1/2(14)
Next, solve the multiplication part, so it now looks like this: 0 + 7
Solve that and the answer is 7.
3. A jogger runs 4 miles on Monday, 5 miles on
Tuesday, 3 miles on Wednesday, and 5 miles on
Thursday. He doesn't run on Friday. How many
miles did he run in all?
Answer:
17 miles
Step-by-step explanation:
4+5+5+3=17
Cases Prudence has a special (cubic) die. The values on its face are the integers from 1 to 6, but they are not arranged ae in a normal die. When Prudence first tosses the die, the sum of the values on the four side faces is 15. In her second toss, the sum of these values is 12. Find what value appears in the face opposite 6 on Prudence’s special die. (Hint: what are possible values for the top and bottom face when the sum of the side faces is 12).
Answer: 3
Step-by-step explanation:
first, we know that:
1 + 2 + 3 + 4 +5 +6 = 21
Now, which two numbers we should take out in order to have 15?
we can remove the 2 and the 4, or the 1 and the 5.
so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)
in the other arrange, we have that removing two numbers we should get 12.
in order to reach 12, we should remove two numbers that add 9 together.
those can be 4 and 5, or 6 and 3.
Now, notice that in the first restriction we have that:
Or 2 and 4 are opposite,
or 1 and 5 are opposite.
So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.
Then we can affirm that the value that appears in the face opposite to the 6, is the 3.
Find the surface area of the figure. ft
Answer:
486
Step-by-step explanation:
Hello!
To find the surface area of a cube we use the equation
[tex]S = 6a^{2}[/tex]
S is the surface area
a is the side length
Put what we know into the equation
[tex]S = 6*9^{2}[/tex]
Solve
S = 6 * 81
S = 486
Hope this Helps!
Answer:486[tex]ft^{2}[/tex]
Step-by-step explanation:
surface area= 6[tex]l^{2}[/tex]
l=9
sa=6 ([tex]9^{2}[/tex])= 6 x 81=486[tex]ft^{2}[/tex]
The dot plot represents a sampling of ACT scores: dot plot titled ACT Scores with Score on the x axis and Number of Students on the y axis with 1 dot over 24, 3 dots over 26, 3 dots over 27, 5 dots over 28, 3 dots over 30, 3 dots over 32, 1 dot over 35 Which box plot represents the dot plot data? box plot titled ACT Score with a minimum of 24, quartile 1 of 25, median of 26, quartile 3 of 29, and maximum of 35 box plot titled ACT Score with a minimum of 23, quartile 1 of 25, median of 26, quartile 3 of 29, and maximum of 36 box plot titled ACT Score with a minimum of 23, quartile 1 of 27, median of 30, quartile 3 of 34, and maximum of 36 box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35
Answer:
box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35
Step-by-step explanation:
The scores of the students represented on the dot plot are:
1 dot => 24
3 dots => 26, 26, 26
3 dots => 27, 27, 27
5 dots => 28, 28, 28, 28, 28
3 dots => 30, 30, 30
3 dots => 32, 32, 32
1 dot => 35
Quickly, we can ascertain 3 values from these data points of which we can use to find out which box plot represents the dot plot data.
The minimum score = 24
The maximum score = 35
The median score is the 10th value, which is the middle value of the data point = 28
Therefore, we can conclude that: "box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35".
first second and last term of Ap are a,b,2a respectively, find its sum
Answer:
(3ab)/(2(b-a))
Step-by-step explanation:
The n-th term of an arithmetic progression is ...
an = a1 +d(n -1)
Then the value of n is ...
n = (an -a1)/d +1
The sum of an arithmetic progression is the product of the number of terms and the average of the first and last terms. In this sequence, the common difference d is ...
d = (b -a)
So, the sum is ...
Sn = (a +2a)/2·((2a -a)/(b -a) +1)
Sn = (3ab)/(2(b-a)) . . . . sum of the arithmetic progression
__
Example:
The sequence 1, 1.5, 2 has ...
a = 1, b = 1.5
Its sum is given by the above formula as ...
Sn = 3(1)(1.5)/(2(1.5 -1)) = 4.5/(2(.5)) = 4.5 = 1 + 1.5 + 2 . . . . yes
What is the slope of the line?
A. −9/5
B. 5/9
C. −5/9
D. 9/5
Answer: -9/5
Step-by-step explanation: To find the slope, we must understand that the slope of a line is defined as the ratio rise/run.
The rise is the vertical direction of the line and the
run is the horizontal direction of the line.
So to start, I am going to pick 2 points on this line.
You want to find points where the line crosses the four corners.
In the diagram, those would be the points (-4, 5) and (1, -4).
Now, we can use slope formula.
Slope = y₂ - y₁ / x₂ - x₁
So we have -4 - 5/1 - -4 which simplifies to -9/5.
So the slope is -9/5.
Answer:
the answer is -9/5 100%
Step-by-step explanation:
Choose the inequality that represents the following graph.
Answer:
option a
Step-by-step explanation:
give person above brainliest :)
Write a rational number in fraction form that is equivalent to -1.\overline{5}
Answer:
[tex]\dfrac{-14}{9}[/tex].
Step-by-step explanation:
The given number is [tex]-1.\overline{5}[/tex].
We need to find a rational number in fraction form that is equivalent to given number.
Let [tex]x=-1.\overline{5}[/tex]
[tex]x=-1.555...[/tex] ...(1)
Multiply both sides by 10.
[tex]10x=-15.555...[/tex] ...(2)
Subtracting (1) from (2), we get
[tex]10x-x=-15.555...-(-1.555...)[/tex]
[tex]9x=-14[/tex]
Divide both sides by 9.
[tex]x=\dfrac{-14}{9}[/tex]
Therefore, the required rational number is [tex]\dfrac{-14}{9}[/tex].
What is (2/3 x 3/5) - (3/4 x 1/6)
Answer:
2/3×3/5=2/3. 3/4×1/6=1/8
2/3-1/8=11/40
Answer:
[tex] \boxed{ \frac{11}{40} }[/tex]Step-by-step explanation:
[tex]( \frac{2}{3} \times \frac{3}{5} ) - ( \frac{3}{4} \times \frac{1}{6} )[/tex]
Reduce the numbers with Greatest common factor 3
⇒[tex] \mathsf{(2 \times \frac{1}{5} ) - ( \frac{1}{4} \times \frac{1}{2} )}[/tex]
Calculate the product
⇒[tex] \mathsf{( \frac{2}{5} )- ( \frac{1}{4} \times \frac{1}{2}) }[/tex]
Subtract the fractions
⇒[tex] \mathsf{ \frac{2 \times 8 - 1 \times 5}{40} }[/tex]
⇒[tex] \mathsf{ \frac{16 - 5}{40} }[/tex]
⇒[tex] \mathsf{ \frac{11}{40} }[/tex]
Hope I helped!
Best regards!
Which of the following statements is false?
If a number is an integer, then it is irrational.
If a number is a natural number, then it is rational.
If a number is a fraction, then it is rational.
If a number is a whole number, then it is rational.
Answer:
If a number is an integer, then it is irrational. ⇒ false statement
Step-by-step explanation:
Let's check:
If a number is an integer, then it is irrational.
- incorrect, as all integers are rational
If a number is a natural number, then it is rational.
- correct, natural numbers are subset of rational numbers
If a number is a fraction, then it is rational.
- correct, they can be shown as p/q
If a number is a whole number, then it is rational.
- correct, whole numbers are subset of rational numbers
The statement "If a number is an integer, then it is irrational" is false.
Which of the following statements is false?The statement "If a number is an integer, then it is irrational" is false. This is because not all integers are irrational.
The other statements are all true:
"If a number is a natural number, then it is rational." This is true because all natural numbers are integers, and all integers are rational.
"If a number is a fraction, then it is rational." This is true because a fraction is a number of the form p/q, where p and q are integers and q is not equal to 0. Any number of this form is rational.
"If a number is a whole number, then it is rational." This is true because all whole numbers are integers, and all integers are rational.
Therefore, the false statement is the first one: "If a number is an integer, then it is irrational."
Below is a table summarizing the statements:
Statement Truth value
If a number is an integer, then it is irrational False
If a number is a natural number, then it is rational True
If a number is a fraction, then it is rational True
If a number is a whole number, then it is rational True
Learn more about rational numbers on:
brainly.com/question/22221295
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A study was conducted by a research center. It reported that most shoppers have a specific spending limit in place while shopping online. The reports indicate that men spend an average of $240 online before they decide to visit a store. If the spending limit is normally distributed and the standard deviation is $20.
A. Find the probability that a male spent less than $210 online before deciding to visit a store.
B. Find the probability that a male spent between $270 and $300 online before deciding to visit a store.
C. Ninety percent of the amounts spent online by a male before deciding to visit a store are less than what value?
Answer:
(A) The probability that a male spent less than $210 online before deciding to visit a store is 0.0668.
(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is 0.0655.
(C) Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.
Step-by-step explanation:
We are given that the reports indicate that men spend an average of $240 online before they decide to visit a store. If the spending limit is normally distributed and the standard deviation is $20.
Let X = the spending limit
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean spending limit = $240
[tex]\sigma[/tex] = standard deviation = $20
So, X ~ Normal([tex]\mu=\$240,\sigma^{2} =\$20^{2}[/tex])
(A) The probability that a male spent less than $210 online before deciding to visit a store is given by = P(X < $210)
P(X < $210) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$210-\$240}{\$20}[/tex] ) = P(Z < -1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)
= 1 - 0.9332 = 0.0668
The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.
(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is given by = P($270 < X < $300)
P($270 < X < $300) = P(X < $300) - P(X [tex]\leq[/tex] $270)
P(X < $300) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$300-\$240}{\$20}[/tex] ) = P(Z < 3) = 0.9987
P(X [tex]\leq[/tex] $270) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$270-\$240}{\$20}[/tex] ) = P(Z [tex]\leq[/tex] 1.50) = 0.9332
The above probability is calculated by looking at the value of x = 3 and x = 1.50 in the z table which has an area of 0.9987 and 0.9332 respectively.
Therefore, P($270 < X < $300) = 0.9987 - 0.9332 = 0.0655.
(C) Now, we have to find ninety percent of the amounts spent online by a male before deciding to visit a store is less than what value, that is;
P(X < x) = 0.90 {where x is the required value}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-\$240}{\$20}[/tex] ) = 0.90
P(Z < [tex]\frac{x-\$240}{\$20}[/tex] ) = 0.90
In the z table, the critical value of z that represents the bottom 90% of the area is given as 1.2816, i.e;
[tex]\frac{x-\$240}{\$20}=1.2816[/tex]
[tex]x-240=1.2816\times 20[/tex]
[tex]x=240 + 25.632[/tex]
x = 265.632
Hence, Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.
Evaluate 26 + a if a = 8
Answer:
34
Step-by-step explanation:
= 26 + 8
= 34
1/3 is part of which set of numbers?
Answer:
[tex] \frac{1}{3} [/tex]Rational number as denominator is not equal to zero and numerator is a integer.
Rational numbers. denoted by [tex] \mathbb Q[/tex]
1/3 is clearly not a natural number or integer.
it is a fraction, =0.333 , it fits the definition of rational number ([tex] \frac pq [/tex]).
Solve for x: x/25 > 5
Answer:
x>125
Step-by-step explanation:
Answer:
x > 125
Step-by-step explanation:
Multiply each side by 25, so it now looks like this: x > 125I hope this helps!
Please answer this correctly without making mistakes
Answer: 139/7
Step-by-step explanation:
Answer:
139/7
Step-by-step explanation:
182/10 = 18.2 < 18 7/11
219/12 = 18 + 3/12 = 18 1/4 < 18 7/11
139/7 = 19 + 4/7 > 18 7/11
179/10 = 17.9 < 18 7/11
quanto e 45x12 (500-450-550)
Answer:
see below
Step-by-step explanation:
the simple answer is -270000
Smoking by Race for Males Aged 18-24
Smoker Nonsmoker Row Total
(S) (N)
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
Calculate the probabilities given below (Round your answers to 4 decimal places.):
i. P(S) 0.3200
ii. P(W) 0.8500
iii. P(S | W) 0.2720
iv. P(S | B) 0.0300
v. P(S and W) 0.9062
vi. P(N and B) 0.1765
Answer:
(i) 0.32 (ii) 0.85
(iii) 0.3412 (iv) 0.20
(v) 0.29 (vi) 0.12
Step-by-step explanation:
The data provided is as follows:
Race Smoker (S) Nonsmoker (N) Row Total
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
(i)
Compute the value of P (S) as follows:
[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]
P (S) = 0.32.
(ii)
Compute the value of P (W) as follows:
[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]
P (W) = 0.85.
(iii)
Compute the value of P (S|W) as follows:
[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]
P (S|W) = 0.3412.
(iv)
Compute the value of P (S|B) as follows:
[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]
P (S|W) = 0.20.
(v)
Compute the value of P (S∩W) as follows:
[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]
P (S∩W) = 0.29.
(vi)
Compute the value of P (N∩B) as follows:
[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]
P (S∩W) = 0.12.
