Question 1

Suppose $x$ is a uniform random variable with $c = 20$ and $d = 90$. Find the standard deviation of $x$.

Accepted Answer

A)  $\sigma = 31.75$ 
B)  $\sigma = 2.42$ 
C)  $\sigma = 3.03$ 
D)  $\sigma = 20.21$ 
A)  $\sigma = 31.75$ 
B)  $\sigma = 2.42$ 
C)  $\sigma = 3.03$ 
D)  $\sigma = 20.21$

Question 2

Consider the given discrete probability distribution. Find $P ( x  3 ) \text {. }$
 $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 1 & 2 & 3 & 4 & 5 \
\hline p ( x ) & .1 & .2 & .2 & .3 & .2 \
\hline
\end{array}$$

Accepted Answer

The answer of Consider the given discrete probability distribution. Find...

Question 3

We believe that 81% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 39 students from the population. How many of the sampled students do we expect to consider statistics to be an exciting subject?

Accepted Answer

A)  39 
B)  31.59 
C)  33.82 
D)  32.16 
A)  39 
B)  31.59 
C)  33.82 
D)  32.16

Question 4

The exponential distribution has the property that its mean equals its standard deviation.

Accepted Answer

A) True 
 B)False

Question 5

An automobile manufacturer has determined that 30% of all gas tanks that were installed on its 2002 compact model are defective. If 13 of these cars are independently sampled, what is the probability that more than half need new gas tanks?

Accepted Answer

Let @#LAT-DLM& the number of the 13 cars

Question 6

The conditions for both the hypergeometric and the binomial random variables require that the trials are independent.

Accepted Answer

A) True 
 B)False

Question 7

When the points on a normal probability plot lie approximately on a straight line, the data are approximately normally distributed.

Accepted Answer

A) True 
 B)False

Question 8

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 61°F to 86°F. What is the probability that the high temperature on a day in August exceeds 66°F?

Accepted Answer

A)  0.449 
B)  0.04 
C)  0.8 
D)  0.2 
A)  0.449 
B)  0.04 
C)  0.8 
D)  0.2

Question 9

If x is a binomial random variable, com $$\mathrm { p } ( \mathrm { x } ) \text { for } \mathrm { n } = 3 , \mathrm { x } = 1 , \mathrm { q } = 0.3$$

Accepted Answer

A)  0.4631 
B)  0.1777 
C)  0.4410 
D)  0.1890 
A)  0.4631 
B)  0.1777 
C)  0.4410 
D)  0.1890

Question 10

Suppose that 4 out of 12 liver transplants done at a hospital will fail within a year. Consider a random sample of 3 of these 12 patients. What is the probability that all 3 patients will result in failed transplants?

Accepted Answer

A)  .037 
B)  .018 
C)  .296 
D)  .333 
A)  .037 
B)  .018 
C)  .296 
D)  .333

Question 11

A machine is set to pump cleanser into a process at the rate of 10 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 9.5 to 12.5 gallons per minute. What is the probability that at the time the machine is checked it is pumping more than 11.0 gallons per minute?

Accepted Answer

A)  .25 
B)  .667 
C)  .50 
D)  .7692 
A)  .25 
B)  .667 
C)  .50 
D)  .7692

Question 12

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1300 miles. What is the probability a particular tire of this brand will last longer than 58,700 miles?

Accepted Answer

A)  .2266 
B)  .8413 
C)  .1587 
D)  .7266 
A)  .2266 
B)  .8413 
C)  .1587 
D)  .7266

Question 13

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 8200 miles. If the manufacturer guarantees the tread life of the tires for the first 50,160 miles, what proportion of the tires will need to be replaced under warranty?

Accepted Answer

Let @#LAT-DLM& be the tread life of this

Question 14

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.9. Find the probability of observing exactly four accidents on this stretch of road next month.

Accepted Answer

A)  1.296886 
B)  0.035656 
C)  4.788184 
D)  174.158539 
A)  1.296886 
B)  0.035656 
C)  4.788184 
D)  174.158539

Question 15

Suppose that x has an exponential distribution with $\theta = 2.5 . \text { Find } P ( x \geq 4 ) \text {. }$

Accepted Answer

A)  0.798103 
B)  0.535261 
C)  0.201897 
D)  0.464739 
A)  0.798103 
B)  0.535261 
C)  0.201897 
D)  0.464739

Question 16

An automobile insurance company estimates the following loss probabilities for the nextyear on a $25,000 sports car: 
$$\begin{array} { l l } 
\text { Total loss: } & 0.001 \
50 \% \text { loss: } & 0.01 \
25 \% \text { loss: } & 0.05 \
10 \% \text { loss: } & 0.10 \
\text { No loss: } & 0.839
\end{array}$$ Assuming the company will sell only a $500 deductible policy for this model (i.e., the owner covers the first $500 damage), how much annual premium should the company charge in order to average $565 profit per policy sold?

Accepted Answer

To determine the premium, the insurance

Question 17

For a continuous probability distribution, the probability that $x$ is between a and b is the same regardless of whether or not you include the endpoints, a and b, of the interval.

Accepted Answer

A) True 
 B)False

Question 18

Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, compute the mean of x.

Accepted Answer

A)  1 
B)  3 
C)  2 
D)  4 
A)  1 
B)  3 
C)  2 
D)  4

Question 19

A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Can the normal approximation be used to estimate the binomial distribution in this problem?

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 20

Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$. Find the mean and standard deviation of $x$.

Accepted Answer

A)  $\mu = 1.5 ; \sigma = 1$ 
B)  $\mu = 0 ; \sigma = 1.5$ 
C)  $\mu = 1.5 ; \sigma = 1.5$ 
D)  $\mu = 0 ; \sigma = 1$ 
A)  $\mu = 1.5 ; \sigma = 1$ 
B)  $\mu = 0 ; \sigma = 1.5$ 
C)  $\mu = 1.5 ; \sigma = 1.5$ 
D)  $\mu = 0 ; \sigma = 1$

Suppose $x$ is a uniform random variable with $c = 20$ and $d = 90$ . Find the standard deviation of $x$ .

Consider the given discrete probability distribution. Find $P ( x < 2 \text { or } x > 3 ) \text {. }$ x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

We believe that 81% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 39 students from the population. How many of the sampled students do we expect to consider statistics to be an exciting subject?

The exponential distribution has the property that its mean equals its standard deviation.

An automobile manufacturer has determined that 30% of all gas tanks that were installed on its 2002 compact model are defective. If 13 of these cars are independently sampled, what is the probability that more than half need new gas tanks?

The conditions for both the hypergeometric and the binomial random variables require that the trials are independent.

When the points on a normal probability plot lie approximately on a straight line, the data are approximately normally distributed.

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 61°F to 86°F. What is the probability that the high temperature on a day in August exceeds 66°F?

If x is a binomial random variable, com $\mathrm { p } ( \mathrm { x } ) \text { for } \mathrm { n } = 3 , \mathrm { x } = 1 , \mathrm { q } = 0.3$

Suppose that 4 out of 12 liver transplants done at a hospital will fail within a year. Consider a random sample of 3 of these 12 patients. What is the probability that all 3 patients will result in failed transplants?

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1300 miles. What is the probability a particular tire of this brand will last longer than 58,700 miles?

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.9. Find the probability of observing exactly four accidents on this stretch of road next month.

Suppose that x has an exponential distribution with $\theta = 2.5 . \text { Find } P ( x \geq 4 ) \text {. }$

For a continuous probability distribution, the probability that $x$ is between a and b is the same regardless of whether or not you include the endpoints, a and b, of the interval.

Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, compute the mean of x.

A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Can the normal approximation be used to estimate the binomial distribution in this problem?

Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$ . Find the mean and standard deviation of $x$ .

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

Suppose xxx is a uniform random variable with c=20c = 20c=20 and d=90d = 90d=90 . Find the standard deviation of xxx .

Consider the given discrete probability distribution. Find P(x<2 or x>3). P ( x < 2 \text { or } x > 3 ) \text {. }P(x<2 or x>3). x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

We believe that 81% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 39 students from the population. How many of the sampled students do we expect to consider statistics to be an exciting subject?

The exponential distribution has the property that its mean equals its standard deviation.

An automobile manufacturer has determined that 30% of all gas tanks that were installed on its 2002 compact model are defective. If 13 of these cars are independently sampled, what is the probability that more than half need new gas tanks?

The conditions for both the hypergeometric and the binomial random variables require that the trials are independent.

When the points on a normal probability plot lie approximately on a straight line, the data are approximately normally distributed.

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 61°F to 86°F. What is the probability that the high temperature on a day in August exceeds 66°F?

If x is a binomial random variable, com p(x) for n=3,x=1,q=0.3\mathrm { p } ( \mathrm { x } ) \text { for } \mathrm { n } = 3 , \mathrm { x } = 1 , \mathrm { q } = 0.3p(x) for n=3,x=1,q=0.3

Suppose that 4 out of 12 liver transplants done at a hospital will fail within a year. Consider a random sample of 3 of these 12 patients. What is the probability that all 3 patients will result in failed transplants?

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1300 miles. What is the probability a particular tire of this brand will last longer than 58,700 miles?

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.9. Find the probability of observing exactly four accidents on this stretch of road next month.

Suppose that x has an exponential distribution with θ=2.5. Find P(x≥4). \theta = 2.5 . \text { Find } P ( x \geq 4 ) \text {. }θ=2.5. Find P(x≥4).

For a continuous probability distribution, the probability that xxx is between a and b is the same regardless of whether or not you include the endpoints, a and b, of the interval.

Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, compute the mean of x.

A study of college students stated that 25% of all college students have at least one tattoo. In a random sample of 80 college students, let x be the number of the students that have at least one tattoo. Can the normal approximation be used to estimate the binomial distribution in this problem?

Suppose that the random variable xxx has an exponential distribution with θ=1.5\theta = 1.5θ=1.5 . Find the mean and standard deviation of xxx .

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

Suppose $x$ is a uniform random variable with $c = 20$ and $d = 90$ . Find the standard deviation of $x$ .

Consider the given discrete probability distribution. Find $P ( x < 2 \text { or } x > 3 ) \text {. }$ x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

If x is a binomial random variable, com $\mathrm { p } ( \mathrm { x } ) \text { for } \mathrm { n } = 3 , \mathrm { x } = 1 , \mathrm { q } = 0.3$

Suppose that x has an exponential distribution with $\theta = 2.5 . \text { Find } P ( x \geq 4 ) \text {. }$

For a continuous probability distribution, the probability that $x$ is between a and b is the same regardless of whether or not you include the endpoints, a and b, of the interval.

Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$ . Find the mean and standard deviation of $x$ .