Answer:
[tex]P(Positive\ Mixture) = 0.2775[/tex]
The probability is not low
Step-by-step explanation:
Given
[tex]P(Single\ Positive) = 0.15[/tex]
[tex]n = 2[/tex]
Required
[tex]P(Positive\ Mixture)[/tex]
First, we calculate the probability of single negative using the complement rule
[tex]P(Single\ Negative) = 1 - P(Single\ Positive)[/tex]
[tex]P(Single\ Negative) = 1 - 0.15[/tex]
[tex]P(Single\ Negative) = 0.85[/tex]
[tex]P(Positive\ Mixture)[/tex] is calculated using:
[tex]P(Positive\ Mixture) = 1 - P(All\ Negative)[/tex] ---- i.e. complement rule
So, we have:
[tex]P(Positive\ Mixture) = 1 - 0.85^2[/tex]
[tex]P(Positive\ Mixture) = 1 - 0.7225[/tex]
[tex]P(Positive\ Mixture) = 0.2775[/tex]
Probabilities less than 0.05 are considered low.
So, we can consider that the probability is not low because 0.2775 > 0.05
Please help!!
Find BD
Answer: [tex]8\sqrt{2}[/tex]
==========================================================
Work Shown:
Focus entirely on triangle ABD (or on triangle BCD; both are identical)
The two legs of this triangle are AB = 8 and AD = 8. The hypotenuse is unknown, so we'll say BD = x.
Apply the pythagorean theorem.
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\x = \sqrt{8^2 + 8^2}\\\\x = \sqrt{2*8^2}\\\\x = \sqrt{8^2*2}\\\\x = \sqrt{8^2}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]
So that's why the diagonal BD is exactly [tex]8\sqrt{2}\\\\[/tex] units long
Side note: [tex]8\sqrt{2} \approx 11.3137[/tex]
a farmer needs 5 men to clear his farm in 10 days. How many men will he need if he must finish clearing the farm in two days if they work at the same rate?
Answer:
25 workers
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
,
Analyze the key features of the graph of the quadratic function f(x) = –x^2 + 4x – 3.
1. Does the parabola open up or down?
2. Is the vertex a minimum or a maximum?
3. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
9514 1404 393
Answer:
downmaximumx=2; (2, 1), -3Step-by-step explanation:
1. The negative leading coefficient (-2) tells you the parabola opens downward.
__
2. The fact that the parabola opens downward tells you the vertex is a maximum.
__
3. For quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For this parabola, that is x = -4/(2(-1)) = 2. The y-value of the vertex is f(2) = -2^2+4(2)-3 = -4+8-3 = 1. The y-intercept is the constant, c = -3.
axis of symmetry: x = 2vertex: (2, 1)y-intercept: (0, -3)Doyle Company issued $500,000 of 10-year, 7 percent bonds on January 1, 2018. The bonds were issued at face value. Interest is payable in cash on December 31 of each year. Doyle immediately invested the proceeds from the bond issue in land. The land was leased for an annual $125,000 of cash revenue, which was collected on December 31 of each year, beginning December 31, 2018
Answer:
f
Step-by-step explanation:
190 of 7
6 7 8 9 10
-3
4
5
6
The slope of the line shown in the graph is
and the intercept of the line is
Answer:slope 2/3
Y-int 6
Step-by-step explanation:
The PTA sells 100 tickets for a raffle and puts them in a bowl. They will randomly pull out a ticket for the first prize and then another ticket for the second prize. You have 10 tickets and your friend has 10 tickets. What is the probability that your friend wins the first prize and you win the second prize?
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten.
Answer:
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
Step-by-step explanation:
There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.
At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just
[tex]\frac{4}{52}[/tex]
After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is
[tex]\frac{4}{51}[/tex]
Now to get the total probability we need to multiply the two probabilities together
[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]
Solve. x+y+z=6 3x−2y+2z=2−2x−y+3z=−4
Answer:
-4?
hope dis helps ^-^
Use the commutative law of multiplication to rewrite 67 x 13.
A. 3 X 671
B. 13 x 67
C.6 X 7 X1 X3
D.80
Answer:
A. 671*3
B. 67*13
C. 3*1*7*6
D. 1*80
The measure of angle tis 60 degrees.
What is the x-coordinate of the point where the
terminal side intersects the unit circle?
1
2
O
O
Isla Isla
2
DONE
Answer:
Step-by-step explanation:
Not a clear list of options and/or reference frame
Probably 0.5 if angle t is measured from the positive x axis.
If a normally distributed population has a mean (mu) that equals 100 with a standard deviation (sigma) of 18, what will be the computed z-score with a sample mean (x-bar) of 106 from a sample size of 9?
Answer:
Z = 1
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean (mu) that equals 100 with a standard deviation (sigma) of 18
[tex]\mu = 100, \sigma = 18[/tex]
Sample of 9:
This means that [tex]n = 9, s = \frac{18}{\sqrt{9}} = 6[/tex]
What will be the computed z-score with a sample mean (x-bar) of 106?
This is Z when X = 106. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{106 - 100}{6}[/tex]
[tex]Z = 1[/tex]
So Z = 1 is the answer.
Calculus II Question
Identify the function represented by the following power series.
[tex]\sum_{k = 0}^\infty (-1)^k \frac{x^{k + 2}}{4^k}[/tex]
With some rewriting, you get
[tex]\displaystyle \sum_{k=0}^\infty (-1)^k\frac{x^{k+2}}{4^k} = x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k[/tex]
Recall that for |x| < 1, you have
[tex]\displaystyle \frac1{1-x} = \sum_{k=0}^\infty x^k[/tex]
So as long as |-x/4| = |x/4| < 1, or |x| < 4, your series converges to
[tex]\displaystyle x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k = \frac{x^2}{1-\left(-\frac x4\right)} = \frac{x^2}{1+\frac x4} = \boxed{\frac{4x^2}{4+x}}[/tex]
Based on known expressions from Taylor series, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex].
How to derive a function behind the approximated formula by Taylor seriesTaylor series are polynomic approximations used to estimate values both from trascendental and non-trascendental functions. It is commonly used in trigonometric, potential, logarithmic and even rational functions.
In this question we must use series properties and common Taylor series-derived formulas to infer the expression behind the given series. Now we proceed to find the expression:
[tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]
[tex]x^{2}\cdot \sum\limits_{k = 0}^{\infty} \left(-\frac{x}{4} \right)^{k}[/tex]
[tex]x^{2}\cdot \left(\frac{1}{1+\frac{x}{4} } \right)[/tex]
[tex]\frac{4\cdot x^{2}}{4+x}[/tex]
Based on power and series properties and most common Taylor series- derived formulas, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex] represents a Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex]. [tex]\blacksquare[/tex]
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The distance between Ali's house and 1 point
college is exactly 135 miles. If she
drove 2/3 of the distance in 135
minutes. What was her average speed
in miles per hour?
Ali's average speed was 40 miles per hour.
What is an average speed?
The total distance traveled is to be divided by the total time consumed brings us the average speed.
How to calculate the average speed of Ali?
The total distance between the college from Ali's house is 135 miles.
She drove 2/3rd of the total distance in 135 minutes.
She drove =135*2/3miles
=90miles.
Ali can drive 90miles in 135 mins.
Therefore, her average speed is: 90*60/135 miles per hour.
=40 miles per hour.
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the number of multiples of a given number is infinite ( )
Answer:
make an 8 horizontal
oooookkkk
Answer:
TRUE
The number of multiples of a given number is finite is a false statement. The number of multiples of a given number is infinite.
Examples:
Multiples of 2 = 2,4,6,8,10,…..
Multiples of 3 = 3,6,9,12,15,18,…
Multiples of 4 = 4, 8, 12, 16, 120, 24….
∴ The number of multiples of a given number is infinite .
Answer From Gauth Math
can some0ne help me?
Answer:
(x - 2)/3
(x - 4)/-5 or (-x + 4)/5
Step-by-step explanation:
this is an inverse function, and to solve an inverse function you would :
swap x and g(x) without bringing the x coefficient with it, just simply swap the variables. Then, solve for g(x), and that's it
the first question's answer is :
g(x) = 3x + 2
x = 3(g(x)) + 2
x - 2 = 3(g(x))
(x - 2)/3 = g(x)
the second one is:
g(x) = 4 - 5x
x = 4 - 5(g(x))
x - 4 = -5(g(x))
(x-4)/-5 = g(x)
g(x) = 3x + 2
y = 3x + 2
x = 3y + 2
3y = x - 2
y = x/3 - 2/3
inverse g(x) = (x - 2) / 3
g(x) = 4 - 5x
y = 4 - 5x
x = 4 - 5y
5y = 4 - x
y = 4/5 - x/5
inverse g(x) = (4 - x) / 5
[tex]\sqrt{25}[/tex]
Answer:
5
Step-by-step explanation:
Calculate the square root of 25 and get 5.
Tyler and Gabe went to the arcade and played the same two games, Tyler played five rounds of each game for 30$. Write two equations for the amounts the two boys spent. Then find the cost for one round each game.
Equations:
1. (30)(5)= 150
2. 30 + 30 + 30 + 30 + 30 = 150
I round:
30 dollars divided by 5 rounds = 6 dollars per round.
The total amount spent by the two boys is $300.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that Tyler and Gabe went to the arcade and played the same two games. Tyler played five rounds of each game for 30$.
We can write the total amount spent by the two boys as -
total amount = 2 x cost of each game x total number of games played
total amount = 2 x 30 x 5
total amount = 10 x 30
total amount = 300
Therefore, the total amount spent by the two boys is $300.
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Một công ty sản xuất ván trượt có thể bán một cái ván trượt với giá $60.
Tổng chi phí cho sản xuất bao gồm chi phí cố định là $1200 và chi phí để sản xuất một cái ván trượt là $35.
Nếu công ty đó bán được 80 cái ván trượt thì công ty đó
Answer this question that is given
Answer:
See explanation
Step-by-step explanation:
2) (10+4) x 2 = 28
3) (13 + 6) x 2 = 38
4) (8+4) x 2 = 24
5) (11+8) x 2 = 38
Answered by Gauthmath
pls help me asap !!!
Answer:
11
Step-by-step explanation:
Hopefully you can see that this is an isosceles triangle and remembering the inequality theorem of a triangle (4,4,11 triangle cannot exist). Iso triangle has two side the same length - as well as two angles the same.
Solve x∕3 < 5 Question 5 options: A) x ≥ 15 B) x > 15 C) x < 15 D) x ≤ 15
Answer:
C
Step-by-step explanation:
Given
[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )
x < 15 → C
Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print lengths, foot lengths, and heights of males. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on these results, does it appear that police can use a shoe print length to estimate the height of a male? Use a significance level of α=0.01
It does not appear that police can use a shoe print length to estimate the height of a male.
The given parameters are:
[tex]\begin{array}{cccccc}{Shoe\ Print} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ Height (cm) & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]
Rewrite as:
[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]
See attachment for scatter plot
To determine the correlation coefficient, we extend the table as follows:
[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} & y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} & x^2 & {817.96} & {864.36} & {1036.84} & {1049.76} & {745.29} & y^2 & {29756.25} & {31222.89} & {35494.56} & {28934.01} & {32112.64} & x \times y & {4933.5} & {5194.98} & {6066.48} & {5511.24} & {4892.16} \ \end{array}[/tex]
The correlation coefficient (r) is:
[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]
We have:
[tex]n =5[/tex]
[tex]\sum xy =4933.5+5194.98+6066.48+5511.24+4892.16 =26598.36[/tex]
[tex]\sum x =28.6+29.4+32.2+32.4+27.3=149.9[/tex]
[tex]\sum y =172.5+176.7+188.4+170.1+179.2=886.9[/tex]
[tex]\sum x^2 =817.96+864.36+1036.84+1049.76+745.29=4514.21[/tex]
[tex]\sum y^2 =29756.25+31222.89+35494.56+28934.01+32112.64=157520.35[/tex]
Calculate mean of x and y
[tex]\bar x = \frac{\sum x}{n} = \frac{149.9}{5} = 29.98[/tex]
[tex]\bar y = \frac{\sum y}{n} = \frac{886.9}{5} = 177.38[/tex]
Calculate SSx and SSy
[tex]SS_x = \sum (x - \bar x)^2 =(28.6-29.98)^2 + (29.4-29.98)^2 + (32.2-29.98)^2 + (32.4-29.98)^2 + (27.3-29.98)^2 =20.208[/tex]
[tex]SS_y = \sum (y - \bar x)^2 =(172.5-177.38)^2 + (176.7-177.38)^2 + (188.4-177.38)^2 + (170.1-177.38)^2 + (179.2-177.38)^2 =202.028[/tex]
Calculate [tex]\sum(x - \bar x)(y - \bar y)[/tex]
[tex]\sum(x - \bar x)(y - \bar y) = (28.6-29.98)*(172.5-177.38) + (29.4-29.98)*(176.7-177.38) + (32.2-29.98)*(188.4-177.38) + (32.4-29.98)*(170.1-177.38) + (27.3-29.98) *(179.2-177.38) =9.098[/tex]
So:
[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]
[tex]r = \frac{9.098}{\sqrt{20.208 * 202.028}}[/tex]
[tex]r = \frac{9.098}{\sqrt{4082.581824}}[/tex]
[tex]r = \frac{9.098}{63.90}[/tex]
[tex]r = 0.142[/tex]
Calculate test statistic:
[tex]t = \frac{r}{\sqrt{\frac{1 - r^2}{n-2}}}[/tex]
[tex]t = \frac{0.142}{\sqrt{\frac{1 - 0.142^2}{5-2}}}[/tex]
[tex]t = \frac{0.142}{\sqrt{\frac{0.979836}{3}}}[/tex]
[tex]t = \frac{0.142}{\sqrt{0.326612}}[/tex]
[tex]t = \frac{0.142}{0.5715}[/tex]
[tex]t = 0.248[/tex]
Calculate the degrees of freedom
[tex]df = n - 2 = 5 - 2 = 3[/tex]
The [tex]t_{\alpha/2}[/tex] value at:
[tex]df =3[/tex]
[tex]t = 0.248[/tex]
[tex]\alpha = 0.01[/tex]
The value is:
[tex]t_{0.01/2} = \±5.841[/tex]
This means that we reject the null hypothesis if the t value is not between -5.841 and 5.841
We calculate the t value as:
[tex]t = 0.248[/tex]
[tex]-5.841 < 0.248 < 5.841[/tex]
Hence, we do not reject the null hypothesis because they do not appear to have any correlation.
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hlo anyone free .... im bo r ed
d
Step-by-step explanation:
Excuse me! Who r u? where r u frm? tell me tht frst.
Answer:
Oop
Step-by-step explanation:
I’m bored
how many distinct permutations can be formed using the letters of the word robberies
Answer:
45360 arrangements
Step-by-step explanation:
Given the word 'robberies'
Number of letters = 9 letters in total
Repeated letters ; r = 2 ; b = 2 ; e = 2
Therefore, the number of distinct arrangement of letters is :
(total letters)! / repeated letters!
The number of distinct arrangement of letters is :
9! / (2! * 2! * 2!) = (9*8*7*6*5*4*3*2*1) / (2*2*2)
362880 / 8 = 45360 arrangements
Triangles ABC and DEF are similar. Find the missing angles.
please help me on this
Answer:
Median
Step-by-step explanation:
Using the median to measure central tendency, rather than the mean, is better for a skewed data set.
Since a skewed data set will have either very high or low extreme data points, the mean will be less representative and accurate when measuring central tendency.
Using the median will measure this better because it is not as vulnerable as the mean when there are extreme data points.
So, the answer is the median.
Solve this equation for x. Round your answer to the nearest hundredth.
1 = In(x + 7)
Answer:
[tex]\displaystyle x \approx -4.28[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Natural logarithms ln and Euler's number eStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 1 = ln(x + 7)[/tex]
Step 2: Solve for x
[Equality Property] e both sides: [tex]\displaystyle e^1 = e^{ln(x + 7)}[/tex]Simplify: [tex]\displaystyle x + 7 = e[/tex][Equality Property] Isolate x: [tex]\displaystyle x = e - 7[/tex]Evaluate: [tex]\displaystyle x = -4.28172[/tex]e^1 = x+7
e - 7 = x
x = -4.28
A shop sells a particular of video recorder. Assuming that the weekly demand for the video recorder is a Poisson variable with the mean 3, find the probability that the shop sells. . (a) At least 3 in a week. (b) At most 7 in a week. (c) More than 20 in a month (4 weeks).
Answer:
a) 0.5768 = 57.68% probability that the shop sells at least 3 in a week.
b) 0.988 = 98.8% probability that the shop sells at most 7 in a week.
c) 0.0104 = 1.04% probability that the shop sells more than 20 in a month.
Step-by-step explanation:
For questions a and b, the Poisson distribution is used, while for question c, the normal approximation is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of successes
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The Poisson distribution can be approximated to the normal with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex], if [tex]\lambda>10[/tex].
Poisson variable with the mean 3
This means that [tex]\lambda= 3[/tex].
(a) At least 3 in a week.
This is [tex]P(X \geq 3)[/tex]. So
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
So
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0498 + 0.1494 + 0.2240 = 0.4232[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 1 - 0.4232 = 0.5768[/tex]
0.5768 = 57.68% probability that the shop sells at least 3 in a week.
(b) At most 7 in a week.
This is:
[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]
[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]
[tex]P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008[/tex]
[tex]P(X = 6) = \frac{e^{-3}*3^{6}}{(6)!} = 0.0504[/tex]
[tex]P(X = 7) = \frac{e^{-3}*3^{7}}{(7)!} = 0.0216[/tex]
Then
[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008 + 0.0504 + 0.0216 = 0.988[/tex]
0.988 = 98.8% probability that the shop sells at most 7 in a week.
(c) More than 20 in a month (4 weeks).
4 weeks, so:
[tex]\mu = \lambda = 4(3) = 12[/tex]
[tex]\sigma = \sqrt{\lambda} = \sqrt{12}[/tex]
The probability, using continuity correction, is P(X > 20 + 0.5) = P(X > 20.5), which is 1 subtracted by the p-value of Z when X = 20.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 12}{\sqrt{12}}[/tex]
[tex]Z = 2.31[/tex]
[tex]Z = 2.31[/tex] has a p-value of 0.9896.
1 - 0.9896 = 0.0104
0.0104 = 1.04% probability that the shop sells more than 20 in a month.
The probability of the selling the video recorders for considered cases are:
P(At least 3 in a week) = 0.5768 approximately.P(At most 7 in a week) = 0.9881 approximately.P( more than 20 in a month) = 0.0839 approximately.What are some of the properties of Poisson distribution?Let X ~ Pois(λ)
Then we have:
E(X) = λ = Var(X)
Since standard deviation is square root (positive) of variance,
Thus,
Standard deviation of X = [tex]\sqrt{\lambda}[/tex]
Its probability function is given by
f(k; λ) = Pr(X = k) = [tex]\dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]
For this case, let we have:
X = the number of weekly demand of video recorder for the considered shop.
Then, by the given data, we have:
X ~ Pois(λ=3)
Evaluating each event's probability:
Case 1: At least 3 in a week.
[tex]P(X > 3) = 1- P(X \leq 2) = \sum_{i=0}^{2}P(X=i) = \sum_{i=0}^{2} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 3) = 1 - e^{-3} \times \left( 1 + 3 + 9/2\right) \approx 1 - 0.4232 = 0.5768[/tex]
Case 2: At most 7 in a week.
[tex]P(X \leq 7) = \sum_{i=0}^{7}P(X=i) = \sum_{i=0}^{7} \dfrac{3^ie^{-3}}{i!}\\\\P(X \leq 7) = e^{-3} \times \left( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120 + 729/720 + 2187/5040\right)\\\\P(X \leq 7) \approx 0.9881[/tex]
Case 3: More than 20 in a month(4 weeks)
That means more than 5 in a week on average.
[tex]P(X > 5) = 1- P(X \leq 5) =\sum_{i=0}^{5}P(X=i) = \sum_{i=0}^{5} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 5) = 1- e^{-3}( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120)\\\\P(X > 5) \approx 1 - 0.9161 \\ P(X > 5) \approx 0.0839[/tex]
Thus, the probability of the selling the video recorders for considered cases are:
Learn more about poisson distribution here:
https://brainly.com/question/7879375
5x-22 3x +105 x minus 22 3 X + 10
-291x+10
:)))))) Have fun
A rectangle has a length of 7 in. and a width of 2 in. if the rectangle is enlarged using a scale factor of 1.5, what will be the perimeter of the new rectangle
Answer:
27 inch
Step-by-step explanation:
Current perimeter=18
New perimeter=18*1.5=27 in
