Question 1

Explain why the following is or is not a valid probability distribution for the discrete random variable x.

$$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 1 & 0 & 1 & 2 & 3 \
\hline p ( x ) & .1 & .2 & .3 & .3 & .1 \
\hline
\end{array}$$

Accepted Answer

This is a valid probability di

Question 2

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5 Years or more.

Accepted Answer

A)  0.770210 
B)  0.506617 
C)  0.493383 
D)  0.229790 
A)  0.770210 
B)  0.506617 
C)  0.493383 
D)  0.229790

Question 3

A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a binomial probability table to find the probability that more than 10 but fewer than 16 of the 20 eligible voters sampled will vote in the next presidential election.

Accepted Answer

A)  0.714 
B)  0.780 
C)  0.845 
D)  0.649 
A)  0.714 
B)  0.780 
C)  0.845 
D)  0.649

Question 4

The probability density function for an exponential random variable $x$ has a graph called a bell curve.

Accepted Answer

A) True 
 B)False

Question 5

$\text { Compute } \left( \begin{array} { l } 
6 \
2
\end{array} \right) ( .3 ) ^ { 2 } ( .7 ) ^ { 6 - 2 }$

Accepted Answer

\[\left( \begin{array} { l }

Question 6

Calculate the mean for the discrete probability distribution shown here. $$\begin{array} { l | c c c c } 
X & 2 & 6 & 9 & 14 \
\hline P ( X ) & .2 & .3 & .3 & .2
\end{array}$$

Accepted Answer

\[\begin{aligned}
\mu & = \sum

Question 7

Suppose that x has an exponential distribution with $\theta = 1.75 .$ Find each probability. 
a. $P ( x \geq 2 )$
b. $P ( x < 2 )$

Accepted Answer

The answer of Suppose that x has an exponential distribution...

Question 8

The waiting time (in minutes) between ordering and receiving your meal at a certain restaurant is exponentially distributed with a mean of 10 minutes. The restaurant has a policy that your meal is free if you have to wait more than 25 minutes after ordering. What is the probability of receiving a free meal?

Accepted Answer

A)  0.917915 
B)  0.329680 
C)  0.082085 
D)  0.670320 
A)  0.917915 
B)  0.329680 
C)  0.082085 
D)  0.670320

Question 9

It is against the law to discriminate against job applicants because of race, religion, sex, or age. Of the individuals who apply for an accountant's position in a large corporation, 38 are over 45 years old. If the company decides to choose 88 of a very large number of applicants for closer credential screening, claiming that the selection will be random and not age-biased, what is the $z$-value associated with fewer than 42 of those chosen being over 45 years old? (Assume that the applicant pool is large enough so that $x$, the number in the sample over 45 years old, has a binomial probability distribution.)

Accepted Answer

@#LAT-DLM& is a bino

Question 10

For a standard normal random variable, find the point in the distribution in which $11.9 \%$ of the z-values fall below.

Accepted Answer

A)  $1.18$ 
B)  $- 0.30$ 
C)  $- 1.45$ 
D)  $- 1.18$ 
A)  $1.18$ 
B)  $- 0.30$ 
C)  $- 1.45$ 
D)  $- 1.18$

Question 11

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 30 to 80. What is the mean outcome of this experiment?

Accepted Answer

A)  30 
B)  60 
C)  80 
D)  55 
A)  30 
B)  60 
C)  80 
D)  55

Question 12

If a data set is normally distributed, what is the proportion of measurements you would expect to fall within $\mu \pm \sigma$ ?

Accepted Answer

A)  100% 
B)  50% 
C)  68% 
D)  95% 
A)  100% 
B)  50% 
C)  68% 
D)  95%

Question 13

Suppose x is a uniform random variable with c = 20 and d = 80. Find P(x > 38).

Accepted Answer

A)  0.1 
B)  0.7 
C)  0.3 
D)  0.9 
A)  0.1 
B)  0.7 
C)  0.3 
D)  0.9

Question 14

A machine is set to pump cleanser into a process at the rate of 7 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 9.5 gallons per minute. Find the probability that between 7.0 gallons and 8.0 gallons are pumped during a randomly selected minute.

Accepted Answer

A)  1 
B)  0.33 
C)  0 
D)  0.67 
A)  1 
B)  0.33 
C)  0 
D)  0.67

Question 15

The weight of corn chips dispensed into a 48-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 48.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 48-ounce bags contain more than the advertised 48 ounces of chips?

Accepted Answer

A)  .5062 
B)  .9938 
C)  .0062 
D)  .4938 
A)  .5062 
B)  .9938 
C)  .0062 
D)  .4938

Question 16

Given that $x$ is a hypergeometric random variable with $N = 8 , n = 4$, and $r = 3$, compute the variance of $x$.

Accepted Answer

A)  .732 
B)  .700 
C)  .469 
D)  .538 
A)  .732 
B)  .700 
C)  .469 
D)  .538

Question 17

If x is a binomial random variable, calculate $\sigma ^ { 2 } \text { for } n = 40 \text { and } p = 0.3 \text {. }$

Accepted Answer

A)  12 
B)  3.6 
C)  2.898 
D)  8.4 
A)  12 
B)  3.6 
C)  2.898 
D)  8.4

Question 18

The rate of return for an investment can be described by a normal distribution with mean 28% and standard deviation 3%. What is the probability that the rate of return for the investment exceeds 34%?

Accepted Answer

Let @#LAT-DLM& be the rate of return. Th

Question 19

Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let $x =$ the number of the paint cans selected that are defective. Unknown to the man, $x$ follows a hypergeometric distribution. Find the probability that none of the four cans selected contains an incorrect mix of paint.

Accepted Answer

A)  0.01818 
B)  0.25455 
C)  0.21818 
D)  0.50909 
A)  0.01818 
B)  0.25455 
C)  0.21818 
D)  0.50909

Question 20

Transportation officials tell us that 90% of drivers wear seat belts while driving. Find the probability that more than 551 drivers in a sample of 600 drivers wear seat belts.

Accepted Answer

A)  0.1 
B)  0.9 
C)  0.9406 
D)  0.0594 
A)  0.1 
B)  0.9 
C)  0.9406 
D)  0.0594

Explain why the following is or is not a valid probability distribution for the discrete random variable x. x 1 0 1 2 3 p(x) .1 .2 .3 .3 .1

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5 Years or more.

The probability density function for an exponential random variable $x$ has a graph called a bell curve.

$\text { Compute } \left( \begin{array} { l } 6 \\2\end{array} \right) ( .3 ) ^ { 2 } ( .7 ) ^ { 6 - 2 }$

Calculate the mean for the discrete probability distribution shown here. X 2 6 9 14 P(X) .2 .3 .3 .2

Suppose that x has an exponential distribution with $\theta = 1.75 .$ Find each probability. a. $P ( x \geq 2 )$ b. $P ( x < 2 )$

For a standard normal random variable, find the point in the distribution in which $11.9 \%$ of the z-values fall below.

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 30 to 80. What is the mean outcome of this experiment?

If a data set is normally distributed, what is the proportion of measurements you would expect to fall within $\mu \pm \sigma$ ?

Suppose x is a uniform random variable with c = 20 and d = 80. Find P(x > 38).

The weight of corn chips dispensed into a 48-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 48.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 48-ounce bags contain more than the advertised 48 ounces of chips?

Given that $x$ is a hypergeometric random variable with $N = 8 , n = 4$ , and $r = 3$ , compute the variance of $x$ .

If x is a binomial random variable, calculate $\sigma ^ { 2 } \text { for } n = 40 \text { and } p = 0.3 \text {. }$

The rate of return for an investment can be described by a normal distribution with mean 28% and standard deviation 3%. What is the probability that the rate of return for the investment exceeds 34%?

Transportation officials tell us that 90% of drivers wear seat belts while driving. Find the probability that more than 551 drivers in a sample of 600 drivers wear seat belts.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Exam 4: Random Variables and Probability Distributions

Explain why the following is or is not a valid probability distribution for the discrete random variable x. x 1 0 1 2 3 p(x) .1 .2 .3 .3 .1

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5 Years or more.

The probability density function for an exponential random variable xxx has a graph called a bell curve.

Compute (62)(.3)2(.7)6−2\text { Compute } \left( \begin{array} { l } 6 \\2\end{array} \right) ( .3 ) ^ { 2 } ( .7 ) ^ { 6 - 2 } Compute (62​)(.3)2(.7)6−2

Calculate the mean for the discrete probability distribution shown here. X 2 6 9 14 P(X) .2 .3 .3 .2

Suppose that x has an exponential distribution with θ=1.75.\theta = 1.75 .θ=1.75. Find each probability. a. P(x≥2)P ( x \geq 2 )P(x≥2) b. P(x<2)P ( x < 2 )P(x<2)

For a standard normal random variable, find the point in the distribution in which 11.9%11.9 \%11.9% of the z-values fall below.

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 30 to 80. What is the mean outcome of this experiment?

If a data set is normally distributed, what is the proportion of measurements you would expect to fall within μ±σ\mu \pm \sigmaμ±σ ?

Suppose x is a uniform random variable with c = 20 and d = 80. Find P(x > 38).

The weight of corn chips dispensed into a 48-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 48.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 48-ounce bags contain more than the advertised 48 ounces of chips?

Given that xxx is a hypergeometric random variable with N=8,n=4N = 8 , n = 4N=8,n=4 , and r=3r = 3r=3 , compute the variance of xxx .

If x is a binomial random variable, calculate σ2 for n=40 and p=0.3. \sigma ^ { 2 } \text { for } n = 40 \text { and } p = 0.3 \text {. }σ2 for n=40 and p=0.3.

The rate of return for an investment can be described by a normal distribution with mean 28% and standard deviation 3%. What is the probability that the rate of return for the investment exceeds 34%?

Transportation officials tell us that 90% of drivers wear seat belts while driving. Find the probability that more than 551 drivers in a sample of 600 drivers wear seat belts.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

The probability density function for an exponential random variable $x$ has a graph called a bell curve.

$\text { Compute } \left( \begin{array} { l } 6 \\2\end{array} \right) ( .3 ) ^ { 2 } ( .7 ) ^ { 6 - 2 }$

Suppose that x has an exponential distribution with $\theta = 1.75 .$ Find each probability. a. $P ( x \geq 2 )$ b. $P ( x < 2 )$

For a standard normal random variable, find the point in the distribution in which $11.9 \%$ of the z-values fall below.

If a data set is normally distributed, what is the proportion of measurements you would expect to fall within $\mu \pm \sigma$ ?

Given that $x$ is a hypergeometric random variable with $N = 8 , n = 4$ , and $r = 3$ , compute the variance of $x$ .

If x is a binomial random variable, calculate $\sigma ^ { 2 } \text { for } n = 40 \text { and } p = 0.3 \text {. }$