Question 1

The number of children in a family can be modelled using a continuous random variable.

Accepted Answer

A) True 
 B)False

Question 2

$$P ( - 1 < x < 0 ) = P ( 0 < x < 1 ) \text { for any random variable } x \text { that is normally distributed. }$$

Accepted Answer

A) True 
 B)False

Question 3

Use the standard normal distribution to find $P ( 0 < z < 2.25 )$

Accepted Answer

A)  .5122 
B)  .8817 
C)  .7888 
D)  .4878 
A)  .5122 
B)  .8817 
C)  .7888 
D)  .4878

Question 4

Consider the given discrete probability distribution.

$\begin{array}{|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 \
\hline p(x) & .1 & .2 & .2 & .3 & .2 \
\hline
\end{array}$
a. Find $\mu = E ( x )$.
b. Find $\sigma = \sqrt { E \left[ ( x - \mu ) ^ { 2 } \right] }$.
c. Find the probability that the value of $x$ falls within one standard deviation of the mean. Compare this result to the Empirical Rule.

Accepted Answer

a. @#LAT-DLM&
b. @#LAT-DLM&
c. @#LAT-DLM&; The Empirical Rule states t

Question 5

Given that $x$ is a hypergeometric random variable, compute $p ( x ) \text { for } N = 6 , n = 3 , r = 3 \text {, and } x = 1 \text {. }$

Accepted Answer

A)  .375 
B)  .55 
C)  .125 
D)  .45 
A)  .375 
B)  .55 
C)  .125 
D)  .45

Question 6

Consider the given discrete probability distribution. Find the probability that x equals 4. $$\begin{array} { l | c c c c } 
x & 2 & 4 & 7 & 8 \
\hline P ( x ) & 0.24 & ? & 0.28 & 0.01
\end{array}$$

Accepted Answer

A)  0.53 
B)  1.88 
C)  2.12 
D)  0.47 
A)  0.53 
B)  1.88 
C)  2.12 
D)  0.47

Question 7

$\text { Compute } \left( \begin{array} { l } 
5 \
0
\end{array} \right)$

Accepted Answer

A)  10 
B)  1 
C)  5 
D)  undefined 
A)  10 
B)  1 
C)  5 
D)  undefined

Question 8

Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $700 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the point in the distribution
Below which 2.5% of the PCE's fell.

Accepted Answer

A)  $17.50 
B)  $682.50 
C)  $798.00 
D)  $602.00 
A)  $17.50 
B)  $682.50 
C)  $798.00 
D)  $602.00

Question 9

You are performing a study about the weight of preschoolers. A previous study found the weights to be normally distributed with a mean of 30 pounds and a standard deviation of 4 pounds. You randomly sample 30 preschool children and find their weights (in pounds) to be as follows. $$\begin{array} { l l l l l l l l l l } 
25 & 25 & 26 & 26.5 & 27 & 27 & 27.5 & 28 & 28 & 28.5 \
29 & 29 & 30 & 30 & 30.5 & 31 & 31 & 32 & 32.5 & 32.5 \
33 & 33 & 34 & 34.5 & 35 & 35 & 37 & 37 & 38 & 38
\end{array}$$ 
Draw a histogram to display the data. Is it reasonable to assume that the weights are normally distributed? Why?

Accepted Answer

@#IMG-DLM&
 It is not reasonable to assu

Question 10

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. What proportion of the milk vendors had prices that were less than $3.075 per gallon?

Accepted Answer

A)  0.8944 
B)  0.2112 
C)  0.3944 
D)  0.1056 
A)  0.8944 
B)  0.2112 
C)  0.3944 
D)  0.1056

Question 11

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 12 elements containing 7 successes. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all possible values of $X$

Accepted Answer

A) True 
 B)False

Question 12

A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml) and a standard deviation of 0.4 ml. Answer the following questions based on this information.
What proportion of the paint cans contain less than 5.54 ml of the dye?

Accepted Answer

A)  0.9115 
B)  0.9885 
C)  0.5885 
D)  0.0885 
A)  0.9115 
B)  0.9885 
C)  0.5885 
D)  0.0885

Question 13

We believe that 95% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 21 students from the population. If the true percentage is really 95%, find the probability of observing 20 or more students who consider statistics to be an exciting subject. Round to six decimal places.

Accepted Answer

A)  0.716972 
B)  0.340562 
C)  0.283028 
D)  0.376410 
A)  0.716972 
B)  0.340562 
C)  0.283028 
D)  0.376410

Question 14

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 5$. Find the $z$-score that corresponds to the value $x = 60$.

Accepted Answer

A)  5 
B)  12 
C)  0 
D)  1 
A)  5 
B)  12 
C)  0 
D)  1

Question 15

A bank offers online banking to its customers free of charge. While online, customers can also sign up for additional services that the bank offers. Let $x$ be the number of customers who sign up for additional services online each day. Suppose the distribution of $x$ is approximated well by a Poisson distribution with mean $\lambda = 42.3$. Find $E ( x )$ and interpret its value.

Accepted Answer

@#LAT-DLM&; If the daily numbers of cust

Question 16

It a recent study of college students indicated that 30% of all college students had at least one tattoo. A small private college decided to randomly and independently sample 15 of their students and ask if they have a tattoo. Find the standard deviation for this binomial random variable. Round to the nearest hundredth when necessary.

Accepted Answer

A)  1.77 
B)  3.15 
C)  4.5 
D)  10.5 
A)  1.77 
B)  3.15 
C)  4.5 
D)  10.5

Question 17

Suppose x is a uniform random variable with $$c = 20 \text { and } d = 90 . \text { Find } P ( 23 < x < 85 )$$ Round to the nearest hundredth when necessary.

Accepted Answer

A)  0.5 
B)  0.89 
C)  1 
D)  0.11 
A)  0.5 
B)  0.89 
C)  1 
D)  0.11

Question 18

A discrete random variable $\mathrm { x }$ can assume five possible values: $2,3,5,8,10$. Its probability distribution is shown below. Find the probability for the value of $x = 5$.
$\begin{array}{c|ccccc}
\mathrm{x} & 2 & 3 & 5 & 8 & 10 \
\hline \mathrm{p}(\mathrm{x}) & 0.10 & 0.20 & ? ? ? & 0.30 & 0.10
\end{array}$

Accepted Answer

A)  0.1 
B)  0.7 
C)  0.2 
D)  0.3 
A)  0.1 
B)  0.7 
C)  0.2 
D)  0.3

Question 19

A bottle contains 16 ounces of water. The variable $x$ represents the volume, in ounces, of water remaining in the bottle after the first drink is taken. What are the natural bounds for the values of $x$ ? Is $x$ discrete or continuous? Explain.

Accepted Answer

natural bounds for @#LAT-DLM& : 0 ounces

Question 20

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.8. Find the probability that fewer than three accidents will occur next month on this stretch of road.

Accepted Answer

A)  0.024434 
B)  0.975566 
C)  0.007314 
D)  0.992686 
A)  0.024434 
B)  0.975566 
C)  0.007314 
D)  0.992686

The number of children in a family can be modelled using a continuous random variable.

$P ( - 1 < x < 0 ) = P ( 0 < x < 1 ) \text { for any random variable } x \text { that is normally distributed. }$

Use the standard normal distribution to find $P ( 0 < z < 2.25 )$

Given that $x$ is a hypergeometric random variable, compute $p ( x ) \text { for } N = 6 , n = 3 , r = 3 \text {, and } x = 1 \text {. }$

Consider the given discrete probability distribution. Find the probability that x equals 4. x 2 4 7 8 P(x) 0.24 ? 0.28 0.01

$\text { Compute } \left( \begin{array} { l } 5 \\0\end{array} \right)$

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. What proportion of the milk vendors had prices that were less than $3.075 per gallon?

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 12 elements containing 7 successes. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all possible values of $X$

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 5$ . Find the $z$ -score that corresponds to the value $x = 60$ .

Suppose x is a uniform random variable with $c = 20 \text { and } d = 90 . \text { Find } P ( 23 < x < 85 )$ Round to the nearest hundredth when necessary.

A discrete random variable $\mathrm { x }$ can assume five possible values: $2,3,5,8,10$ . Its probability distribution is shown below. Find the probability for the value of $x = 5$ . 2 3 5 8 10 () 0.10 0.20 ??? 0.30 0.10

A bottle contains 16 ounces of water. The variable $x$ represents the volume, in ounces, of water remaining in the bottle after the first drink is taken. What are the natural bounds for the values of $x$ ? Is $x$ discrete or continuous? Explain.

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.8. Find the probability that fewer than three accidents will occur next month on this stretch of road.

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

The number of children in a family can be modelled using a continuous random variable.

P(−1<x<0)=P(0<x<1) for any random variable x that is normally distributed. P ( - 1 < x < 0 ) = P ( 0 < x < 1 ) \text { for any random variable } x \text { that is normally distributed. }P(−1<x<0)=P(0<x<1) for any random variable x that is normally distributed.

Use the standard normal distribution to find P(0<z<2.25)P ( 0 < z < 2.25 )P(0<z<2.25)

Given that xxx is a hypergeometric random variable, compute p(x) for N=6,n=3,r=3, and x=1. p ( x ) \text { for } N = 6 , n = 3 , r = 3 \text {, and } x = 1 \text {. }p(x) for N=6,n=3,r=3, and x=1.

Consider the given discrete probability distribution. Find the probability that x equals 4. x 2 4 7 8 P(x) 0.24 ? 0.28 0.01

Compute (50)\text { Compute } \left( \begin{array} { l } 5 \\0\end{array} \right) Compute (50​)

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. What proportion of the milk vendors had prices that were less than $3.075 per gallon?

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 12 elements containing 7 successes. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all possible values of XXX

Suppose a random variable xxx is best described by a normal distribution with μ=60\mu = 60μ=60 and σ=5\sigma = 5σ=5 . Find the zzz -score that corresponds to the value x=60x = 60x=60 .

Suppose x is a uniform random variable with c=20 and d=90. Find P(23<x<85)c = 20 \text { and } d = 90 . \text { Find } P ( 23 < x < 85 )c=20 and d=90. Find P(23<x<85) Round to the nearest hundredth when necessary.

A discrete random variable x\mathrm { x }x can assume five possible values: 2,3,5,8,102,3,5,8,102,3,5,8,10 . Its probability distribution is shown below. Find the probability for the value of x=5x = 5x=5 . 2 3 5 8 10 () 0.10 0.20 ??? 0.30 0.10

A bottle contains 16 ounces of water. The variable xxx represents the volume, in ounces, of water remaining in the bottle after the first drink is taken. What are the natural bounds for the values of xxx ? Is xxx discrete or continuous? Explain.

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.8. Find the probability that fewer than three accidents will occur next month on this stretch of road.

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

$P ( - 1 < x < 0 ) = P ( 0 < x < 1 ) \text { for any random variable } x \text { that is normally distributed. }$

Use the standard normal distribution to find $P ( 0 < z < 2.25 )$

Given that $x$ is a hypergeometric random variable, compute $p ( x ) \text { for } N = 6 , n = 3 , r = 3 \text {, and } x = 1 \text {. }$

$\text { Compute } \left( \begin{array} { l } 5 \\0\end{array} \right)$

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 12 elements containing 7 successes. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all possible values of $X$

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 5$ . Find the $z$ -score that corresponds to the value $x = 60$ .

Suppose x is a uniform random variable with $c = 20 \text { and } d = 90 . \text { Find } P ( 23 < x < 85 )$ Round to the nearest hundredth when necessary.

A discrete random variable $\mathrm { x }$ can assume five possible values: $2,3,5,8,10$ . Its probability distribution is shown below. Find the probability for the value of $x = 5$ . 2 3 5 8 10 () 0.10 0.20 ??? 0.30 0.10

A bottle contains 16 ounces of water. The variable $x$ represents the volume, in ounces, of water remaining in the bottle after the first drink is taken. What are the natural bounds for the values of $x$ ? Is $x$ discrete or continuous? Explain.