Answer:
The answer is "Option a".
Step-by-step explanation:
[tex]n= 93 \\\\p= 0.24\\\\\mu=?\\\\ \sigma=?\\\\[/tex]
Using the binomial distribution: [tex]\mu = n\times p = 93 \times 0.24 = 22.32\\\\\sigma = \sqrt{n \times p \times (1-p)}=\sqrt{93 \times 0.24 \times (1-0.24)}=4.1186[/tex]
In this the maximum value which is significantly low, [tex]\mu-2\sigma[/tex], and the minimum value which is significantly high, [tex]\mu+2\sigma[/tex], that is equal to:
[tex]\mu-2\sigma = 22.32 - 2(4.1186) = 14.0828 \approx 14.08\\\\\mu+2\sigma = 22.32 + 2(4.1186) = 30.5572 \approx 30.56[/tex]
A packing plant fills bags with cement. The weight X kg of a bag can be modeled by a normal distribution with mean 50kg and standard deviation 2kg. 4.
a. Find the probability that a randomly selected bag weighs more than 53kg.
b. Find the weight that is exceeded by 98% of the bags.
c. Three bags are selected at random. Find the probability that two weigh more than 53kg and one weighs less than 53kg.
Answer:
a) 0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg.
b) The weight that is exceeded by 98% of the bags is of 45.9 kg.
c) 0.0125 = 1.25% probability that two weigh more than 53kg and one weighs less than 53kg.
Step-by-step explanation:
The first two questions are solved using the normal distribution, while the third is solved using the binomial distribution.
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.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The weight X kg of a bag can be modeled by a normal distribution with mean 50kg and standard deviation 2kg.
This means that [tex]\mu = 50, \sigma = 2[/tex]
a. Find the probability that a randomly selected bag weighs more than 53kg.
This is 1 subtracted by the p-value of Z when X = 53. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{53 - 50}{2}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
1 - 0.9332 = 0.0668.
0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg.
b. Find the weight that is exceeded by 98% of the bags.
This is the 100 - 98 = 2nd percentile, which is X when Z has a p-value of 0.02, so X when Z = -2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.054 = \frac{X - 50}{2}[/tex]
[tex]X - 50 = -2.054*2[/tex]
[tex]X = 45.9[/tex]
The weight that is exceeded by 98% of the bags is of 45.9 kg.
c. Three bags are selected at random. Find the probability that two weigh more than 53kg and one weighs less than 53kg.
0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg means that [tex]p = 0.0668[/tex]
3 bags means that [tex]n = 2[/tex]
Two above 53kg, which means that we want P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{3,2}.(0.0668)^{2}.(0.9332)^{1} = 0.0125[/tex]
0.0125 = 1.25% probability that two weigh more than 53kg and one weighs less than 53kg.
According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50 and that a sample of 30 theaters was randomly selected. What is the probability that the sample mean will be between $7.75 and $8.20
Answer:
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
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.
The average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50.
This means that [tex]\mu = 7.96, \sigma = 0.5[/tex]
Sample of 30:
This means that [tex]n = 30, s = \frac{0.5}{\sqrt{30}}[/tex]
What is the probability that the sample mean will be between $7.75 and $8.20?
This is the p-value of Z when X = 8.2 subtracted by the p-value of Z when X = 7.75.
X = 8.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.2 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = 2.63[/tex]
[tex]Z = 2.63[/tex] has a p-value of 0.9957
X = 7.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{7.75 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = -2.3[/tex]
[tex]Z = -2.3[/tex] has a p-value of 0.0107.
0.9957 - 0.0157 = 0.985
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
A sprinter travels a distance of 200 m in a time of 20.03 seconds.
What is the sprinter's average speed rounded to 4 sf?
Given:
Distance traveled by sprinter = 200 m
Time taken by sprinter = 20.03 seconds
To find:
The sprinter's average speed rounded to 4 sf.
Solution:
We know that,
[tex]\text{Average speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
It is given that, the sprinter travels a distance of 200 m in a time of 20.03 seconds.
[tex]\text{Average speed}=\dfrac{200}{20.03}[/tex]
[tex]\text{Average speed}=9.985022466[/tex]
[tex]\text{Average speed}\approx 9.985[/tex]
Therefore, the average speed of the sprinter is 9.985 m/sec.
Answer:
9.985
Step-by-step explanation:
the point (-2,5) is reflected across the y-axis. which of these is the ordered pair of the image
Answer:(2,5)
Step-by-step explanation: watch this video
https://youtu.be/l78P2Xi68-k
Suppose a sample of 1453 new car buyers is drawn. Of those sampled, 363 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places
Answer:
"0.250" is the appropriate answer.
Step-by-step explanation:
Given:
New car sample,
= 1453
Preferred foreign,
= 363
Now,
The amount of new automobile purchasers preferring foreign cars will be approximated as:
= [tex]\frac{363}{1453}[/tex]
= [tex]0.250[/tex]
Pleaseee Help. What is the value of x in this simplified expression?
(-1) =
(-j)*
1
X
What is the value of y in this simplified expression?
1 1
ky
y =
-10
K+m
+
.10
m т
9514 1404 393
Answer:
x = 7
y = 5
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
__
For a=-j and b=7,
(-j)^-7 = 1/(-j)^7 ⇒ x = 7
For a=k and b=-5,
k^-5 = 1/k^5 ⇒ y = 5
a triangle has sides of 6 m 8 m and 11 m is it a right-angled triangle?
Answer:
No
Step-by-step explanation:
If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.
[tex]6^{2}+8^{2}=c^2[/tex]
If the triangle is a right triangle, c would equal 11
Solve.
[tex]36+64=100[/tex]
Then find the square root of 100.
The square root of 100 is 10, not 11.
So this is not a right triangle.
I hope this helps!
On a shelf at a gaming store, there are three Sony PlayStations and seven Nintendo Wii coasters left. If one gaming system is selected at random, find the probability that the system is a Wii console.
Answer:
hello
as probability is equal to number of favourable outcomes/total number of out comes,
Step-by-step explanation:
=7/10
HOPES THAT IT HELPS YOU
PLEASE MARK ME AS BRAINLIEST
!!!!Please Answer Please!!!!
ASAP!!!!!!
!!!!!!!!!!!!!
Answer:
False
Step-by-step explanation:
well i think that the answer from my calculations
Graph the inequality.
7 <= y - 2x < 12
Answer:
X(-12,-7)
Step-by-step explanation:
This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.
40% of what number is 16.6?
What is the measure of F?
G
65
10
H H
10
A. Cannot be determined
B. 55
C. 75
D65
Answer:
D. 65°
Step-by-step explanation:
It is so because the triangle is isosceles, two identical sides and two equal angles.
Which side of the polygon is exactly 6 units long?
Answer:
AB is correct as It is the shorter parallel line
as the line measures 6 units.
Step-by-step explanation:
The polygon is a trapezoid / (trapezium Eng/Europe)
We see the given coordinates (2, 6) - (-4, 6) = x-6 y 0 = x = 6units
as x always is shown as x - 6 as x= 6
We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6
y = 0 x = 6 = 6 units as its horizontal line.
when y is 6-6 = 0 then we know the line is horizontal for y = 0.
The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.
When looking at diagonal lines we still group the x's and y's and make the fraction whole.
When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.
What is the complete factorization of the polynomial below?
x3 + 8x2 + 17x + 10
A. (x + 1)(x + 2)(x + 5)
B. (x + 1)(x-2)(x-5)
C. (x-1)(x+2)(x-5)
O D. (x-1)(x-2)(x + 5)
Answer: A (x+1)(x+2)(x+5)
Step-by-step explanation:
X+34>55
Solve the inequality and enter your solution as an inequality comparing the variable to a number
Answer:
x > 21
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x + 34 > 55
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 34 on both sides: x > 21A large water tank has two inlet pipes (a large and a small one) and one outlet pipe. It takes
2
hours to fill the tank with the large inlet pipe. On the other hand, it takes
5
hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in
7
hours. Assuming that the tank is initially empty, what fraction will be filled in
1
hour if all three pipes are in operation? Your answer should be a fraction in simplest form, without spaces, e.g. 1/2.
Answer:2x+2
Step-by-step explanation:
Describe the transformation of f(x) to g(x). Pleaseee helllp thank youuuu!!!
The transformation set of [tex]y[/tex] values for function [tex]f[/tex] is [tex][-1,1][/tex] this is an interval to which sine function maps.
You can observe that the interval to which [tex]g[/tex] function maps equals to [tex][-2,0][/tex].
So let us take a look at the possible options.
Option A states that shifting [tex]f[/tex] up by [tex]\pi/2[/tex] would result in [tex]g[/tex] having an interval [tex][-1,1]+\frac{\pi}{2}\approx[0.57,2.57][/tex] which is clearly not true that means A is false.
Let's try option B. Shifting [tex]f[/tex] down by [tex]1[/tex] to get [tex]g[/tex] would mean that has a transformation interval of [tex][-1,1]-1=[-2,0][/tex]. This seems to fit our observation and it is correct.
So the answer would be B. If we shift [tex]f[/tex] down by one we get [tex]g[/tex], which means that [tex]f(x)=\sin(x)[/tex] and [tex]g(x)=f(x)-1=\sin(x)-1[/tex].
Hope this helps :)
The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots plus-or-minus 3 i. What is the other root? Use a graphing calculator and a system of equations. –9 –1 0 1
9514 1404 393
Answer:
(b) -1
Step-by-step explanation:
The graph shows the difference between the two expressions is zero at x=-1.
__
Additional comment
For finding solutions to polynomial equations, I like to put them in the form f(x)=0. Most graphing calculators find zeros (x-intercepts) easily. Sometimes they don't do so well with points where curves intersect. Also, the function f(x) is easily iterated by most graphing calculators in those situations where the root is irrational or needs to be found to best possible accuracy.
Answer:
The answer is b: -1
Step-by-step explanation:
good luck!
If two marbles are selected in succession with replacement, find the probability that both marble is blue.
Answer:
1 / 9
Step-by-step explanation:
Choosing with replacement means that the first draw from the lot is replaced before another is picked '.
Number of Blue marbles = 2
Number of red marbles = 4
Total number of marbles = (2 + 4) = 6
Probability = required outcome / Total possible outcomes
1st draw :
Probability of picking blue = 2 / 6 = 1 /3
2nd draw :
Probability of picking blue = 2 / 6 = 1/3
P(1st draw) * P(2nd draw)
1/3 * 1/3 = 1/9
is x^2+y-15=10 a relation and a function?
Answer:
it is
Step-by-step explanation:
yes, it is. every function is a relation
x²+y-15=10
y=25-x²
The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 123 students surveyed 5 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.
a. The sample needs to be random but we don’t know if it is.
b. The actual count of bike riders is too small.
c. The actual count of those who do not ride a bike to campus is too small.
d. n*^p is not greater than 10.
e. n*(1−^p)is not greater than 10.
Answer:
b. The actual count of bike riders is too small.
d. n*p is not greater than 10.
Step-by-step explanation:
Confidence interval for a proportion:
To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]
Of the 123 students surveyed 5 ride a bike to campus.
Less than 10 successes, that is:
The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.
I dont get what this is asking me to do
Answer:
Step-by-step explanation:
what this statement is saying is that if you have
4 x + 3x^2 + 5 + 8x^2 + 12x + 9
that
3x^2 + 8x^2 = 11x^2
4 x + 12x = 16x
5 + 9 = 14
get added together the final answer would be
in descending order as : 11x^2 + 16x + 14
Find the interval in which y= x2 + 4 is increasing
Answer:
x > 0 and x > -6
[tex]{ \tt{y = {x}^{2} + 4}} \\ { \tt{for \: x > 0 :positive \: integers }} \\ y = 0 < x < {}^{ + } \infin[/tex]
Write the standard form of the equation of the circle with center (−7,10) that passes through the point (−7,7)
Answer:
(x+7)^2+(y-10)^2=9
Step-by-step explanation:
The distance between the two points is sqrt((-7+7)^2+(10-7)^2)=3 which is in turn the radius of the circle
Prove the following identities : i) tan a + cot a = cosec a sec a
Step-by-step explanation:
[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]
[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]
[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]
Question :
tan alpha + cot Alpha = cosec alpha. sec alphaRequired solution :
Here we would be considering L.H.S. and solving.
Identities as we know that,
[tex] \red{\boxed{\sf{tan \: \alpha \: = \: \dfrac{sin \: \alpha }{cos \: \alpha} }}}[/tex][tex] \red{\boxed{\sf{cot \: \alpha \: = \: \dfrac{cos \: \alpha }{sin \: \alpha} }}}[/tex]By using the identities we gets,
[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]
Now, here we would be using the identity of square relations.
[tex]\red{\boxed{ \sf{sin {}^{2} \alpha \: + \: cos {}^{2} \alpha \: = \: 1}}}[/tex]By using the identity we gets,
[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]
[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]
Hence proved..!!(4-1) + (6 + 5) = help plz
Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace length is more than 4.03 inches
Answer:
The answer is "".
Step-by-step explanation:
Please find the complete question in the attached file.
We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval
[tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]
Using formula:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The probability that perhaps the mean shells length of the sample is over 4.03 pounds is
[tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]
Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution
[tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]
the required probability: [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]
Below are the heights (in inches) of students in a third-grade class. Find the median height. 39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48
Given:
The heights (in inches) of students in a third-grade class are:
39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48
To find:
The median height.
Solution:
The given data set is:
39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48
Arrange the data set in ascending order.
37, 39, 40, 42, 42, 45, 47, 47, 48, 48, 48, 49, 49, 51, 52, 53
Here, the number of observations is 16. So, the median of the given data set is:
[tex]Median=\dfrac{\dfrac{n}{2}\text{th term}+\left(\dfrac{n}{2}+1\right)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{\dfrac{16}{2}\text{th term}+\left(\dfrac{16}{2}+1\right)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{8\text{th term}+9\text{th term}}{2}[/tex]
[tex]Median=\dfrac{47+48}{2}[/tex]
[tex]Median=\dfrac{95}{2}[/tex]
[tex]Median=47.5[/tex]
Therefore, the median height of the students is 47.5 inches.
Help me complete the proof!
Answer:
Distributive Property means you can multiply the outside and inside of parenthesis.
Addition Property... means you can add the same value to both sides of the equation without changing it. In this case you add 3x.
Subtraction Property... same as addition property, but with subtraction. In this case subtract 10 from both sides.
Division property... same as addition and subtraction properties but with division. In this case divide both sides by 8.
Technically the addition property can be used for the subtract 10 because you just add -10 and multiplication property could be used for the division, because you just multiply both sides by 1/8, but for the purpose of this equation, you would say subtraction and division.
2/3y = 1/4 what does y equal?
Answer:
Step-by-step explanation:
2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3
