Question 1

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 10$ and $d = 50$. Find $P ( x > 50 )$.

Accepted Answer

A)  0.5 
B)  0.4 
C)  0 
D)  1 
A)  0.5 
B)  0.4 
C)  0 
D)  1

Question 2

The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 8.9. Find the probability that exactly four tickets are written on a randomly selected day.

Accepted Answer

A)  .035656 
B)  .941567 
C)  .058433 
D)  .964344 
A)  .035656 
B)  .941567 
C)  .058433 
D)  .964344

Question 3

Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$. Find the probability that $x$ will assume a value within the interval $\mu \pm 2 \sigma$.

Accepted Answer

A)  .864665 
B)  .716531 
C)  .950213 
D)  .049787 
A)  .864665 
B)  .716531 
C)  .950213 
D)  .049787

Question 4

Which one of the following suggests that the data set is approximately normal?

Accepted Answer

A)  A data set with $Q _ { 1 } = 14 , Q _ { 3 } = 68$, and $s = 41$. 
B)  A data set with $Q _ { 1 } = 105 , Q _ { 3 } = 270$, and $s = 33$. 
C)  A data set with $Q _ { 1 } = 2.2 , Q _ { 3 } = 7.3$, and $s = 2.1$. 
D)  A data set with $Q _ { 1 } = 1330 , Q _ { 3 } = 2940$, and $\mathrm { s } = 2440$. 
A)  A data set with $Q _ { 1 } = 14 , Q _ { 3 } = 68$, and $s = 41$. 
B)  A data set with $Q _ { 1 } = 105 , Q _ { 3 } = 270$, and $s = 33$. 
C)  A data set with $Q _ { 1 } = 2.2 , Q _ { 3 } = 7.3$, and $s = 2.1$. 
D)  A data set with $Q _ { 1 } = 1330 , Q _ { 3 } = 2940$, and $\mathrm { s } = 2440$.

Question 5

Which binomial probability is represented on the screen below?

Accepted Answer

A)  $P ( x  4 )$ 
C)  $P ( x \leq 4 )$ 
D)  $P ( x = 4 )$ 
A)  $P ( x  4 )$ 
C)  $P ( x \leq 4 )$ 
D)  $P ( x = 4 )$

Question 6

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 12$. Find the $z$-score that corresponds to the value $x = 72$.

Accepted Answer

A)  5 
B)  1 
C)  12 
D)  72 
A)  5 
B)  1 
C)  12 
D)  72

Question 7

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 at least one of the four cans selected contains an incorrect mix of paint.

Accepted Answer

A)  0.74545 
B)  0.50909 
C)  0.78182 
D)  0.49091 
A)  0.74545 
B)  0.50909 
C)  0.78182 
D)  0.49091

Question 8

$\text { Compute } \left( \begin{array} { l } 
4 \
4
\end{array} \right)$

Accepted Answer

A)  16 
B)  4 
C)  1 
D)  6 
A)  16 
B)  4 
C)  1 
D)  6

Question 9

Explain why the following is or is not a valid probability distribution for the discrete random variable x. 
$$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 10 & 20 & 30 & 40 & 50 \
\hline p ( x ) & .3 & .2 & .2 & .2 & .2 \
\hline
\end{array}$$

Accepted Answer

This is not a valid probabilit

Question 10

Suppose $x$ is a uniform random variable with $c = 10$ and $d = 80$. Find the mean of the random variable $x$.

Accepted Answer

The answer of Suppose $x$ is a uniform random variable...

Question 11

Which one of the following suggests that the data set is not approximately normal?

Accepted Answer

A) 
  
B)  A data set with IQR $= 752$ and $s = 574$. 
C)  A data set with $68 \%$ of the measurements within $\bar { x } \pm 2 \mathrm {~s}$. 
D) 
  
A) 
  
B)  A data set with IQR $= 752$ and $s = 574$. 
C)  A data set with $68 \%$ of the measurements within $\bar { x } \pm 2 \mathrm {~s}$. 
D)

Question 12

The length of time (in months) that a cashier works for a certain fast food restaurant is exponentially distributed with a mean of 7 months.
a. Find the probability that a cashier works for the restaurant for at least 2 years.
b. Find the probability that a cashier works for the restaurant for less than 1 month.

Accepted Answer

The answer of The length of time (in months) that...

Question 13

Suppose that x has an exponential distribution with $$\theta = 2 \text {. Find } P ( x < 1.5 ) \text {. }$$

Accepted Answer

A)  0.472367 
B)  0.527633 
C)  0.736403 
D)  0.263597 
A)  0.472367 
B)  0.527633 
C)  0.736403 
D)  0.263597

Question 14

Suppose that x has an exponential distribution with $\theta = 1.5 . \text { Find } P ( x > 1 )$

Accepted Answer

A)  0.776870 
B)  0.513417 
C)  0.486583 
D)  0.223130 
A)  0.776870 
B)  0.513417 
C)  0.486583 
D)  0.223130

Question 15

Assume that $x$ is a binomial random variable with $\mathrm { n } = 400$ and $\mathrm { p } = 0.30$. Use a normal approximation to find $P ( x \geq 100 )$.

Accepted Answer

A)  0.9875 
B)  0.5948 
C)  0.9834 
D)  0.4875 
A)  0.9875 
B)  0.5948 
C)  0.9834 
D)  0.4875

Question 16

Determine the value of $e ^ { - a / \theta }$ for $\theta = 2$ and $a = 3$.

Accepted Answer

A)  $4.481689$ 
B)  $- 4.481689$ 
C)  $0.513417$ 
D)  $0.223130$ 
A)  $4.481689$ 
B)  $- 4.481689$ 
C)  $0.513417$ 
D)  $0.223130$

Question 17

A statistician received some data to analyze. The sender of the data suggested that the data was normally distributed. Which of the following methods can be used to determine if the data is, in fact, normally distributed?
I. Construct a histogram and/or stem-and-leaf display of the data and check the shape.
II. Compute the intervals $\bar { x } \pm s , \bar { x } \pm 2 s$, and $\bar { x } \pm 3 s$, and determine the percentage of measurements falling in each. Compare these percentages to $68 \% , 95 \%$, and $100 \%$.
III. Calculate a value of $\frac { \mathrm { IQR } } { \mathrm { s } }$. If this value is approximately $1.3$, then the data is normal.
IV. Construct a normal probability plot of the data. If the points fall on a straight line, then the data is normal.

Accepted Answer

A)  II only 
B)  I only 
C)  IV only 
D)  I, II, III, and IV 
E)  III only 
A)  II only 
B)  I only 
C)  IV only 
D)  I, II, III, and IV 
E)  III only

Question 18

For a standard normal random variable, find the probability that z exceeds the value $- 1.65$

Accepted Answer

A)  0.0495 
B)  0.9505 
C)  0.5495 
D)  0.4505 
A)  0.0495 
B)  0.9505 
C)  0.5495 
D)  0.4505

Question 19

A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 41% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution?

Accepted Answer

A)  Yes, the sample is a random and independent sample. 
B)  No, a binomial distribution requires only two possible outcomes for each experimental unit sampled. 
C)  $\text { Yes, the sample size is } n = 20 \text {. }$ 
D)  No, the employees would not be considered independent in the present sample. 
A)  Yes, the sample is a random and independent sample. 
B)  No, a binomial distribution requires only two possible outcomes for each experimental unit sampled. 
C)  $\text { Yes, the sample size is } n = 20 \text {. }$ 
D)  No, the employees would not be considered independent in the present sample.

Question 20

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. Use a binomial probability table to find the probability that exactly 5 of the students reported that they did have at least one tattoo.

Accepted Answer

A)  0.207 
B)  0.722 
C)  0.218 
D)  0.515 
A)  0.207 
B)  0.722 
C)  0.218 
D)  0.515

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 10$ and $d = 50$ . Find $P ( x > 50 )$ .

Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$ . Find the probability that $x$ will assume a value within the interval $\mu \pm 2 \sigma$ .

Which one of the following suggests that the data set is approximately normal?

Which binomial probability is represented on the screen below?

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 12$ . Find the $z$ -score that corresponds to the value $x = 72$ .

$\text { Compute } \left( \begin{array} { l } 4 \\4\end{array} \right)$

Explain why the following is or is not a valid probability distribution for the discrete random variable x. x 10 20 30 40 50 p(x) .3 .2 .2 .2 .2

Suppose $x$ is a uniform random variable with $c = 10$ and $d = 80$ . Find the mean of the random variable $x$ .

Which one of the following suggests that the data set is not approximately normal?

Suppose that x has an exponential distribution with $\theta = 2 \text {. Find } P ( x < 1.5 ) \text {. }$

Suppose that x has an exponential distribution with $\theta = 1.5 . \text { Find } P ( x > 1 )$

Assume that $x$ is a binomial random variable with $\mathrm { n } = 400$ and $\mathrm { p } = 0.30$ . Use a normal approximation to find $P ( x \geq 100 )$ .

Determine the value of $e ^ { - a / \theta }$ for $\theta = 2$ and $a = 3$ .

For a standard normal random variable, find the probability that z exceeds the value $- 1.65$

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 random variable best described by a uniform probability distribution with c=10c = 10c=10 and d=50d = 50d=50 . Find P(x>50)P ( x > 50 )P(x>50) .

Suppose that the random variable xxx has an exponential distribution with θ=1.5\theta = 1.5θ=1.5 . Find the probability that xxx will assume a value within the interval μ±2σ\mu \pm 2 \sigmaμ±2σ .

Which one of the following suggests that the data set is approximately normal?

Which binomial probability is represented on the screen below?

Suppose a random variable xxx is best described by a normal distribution with μ=60\mu = 60μ=60 and σ=12\sigma = 12σ=12 . Find the zzz -score that corresponds to the value x=72x = 72x=72 .

Compute (44)\text { Compute } \left( \begin{array} { l } 4 \\4\end{array} \right) Compute (44​)

Explain why the following is or is not a valid probability distribution for the discrete random variable x. x 10 20 30 40 50 p(x) .3 .2 .2 .2 .2

Suppose xxx is a uniform random variable with c=10c = 10c=10 and d=80d = 80d=80 . Find the mean of the random variable xxx .

Which one of the following suggests that the data set is not approximately normal?

Suppose that x has an exponential distribution with θ=2. Find P(x<1.5). \theta = 2 \text {. Find } P ( x < 1.5 ) \text {. }θ=2. Find P(x<1.5).

Suppose that x has an exponential distribution with θ=1.5. Find P(x>1)\theta = 1.5 . \text { Find } P ( x > 1 )θ=1.5. Find P(x>1)

Assume that xxx is a binomial random variable with n=400\mathrm { n } = 400n=400 and p=0.30\mathrm { p } = 0.30p=0.30 . Use a normal approximation to find P(x≥100)P ( x \geq 100 )P(x≥100) .

Determine the value of e−a/θe ^ { - a / \theta }e−a/θ for θ=2\theta = 2θ=2 and a=3a = 3a=3 .

For a standard normal random variable, find the probability that z exceeds the value −1.65- 1.65−1.65

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 random variable best described by a uniform probability distribution with $c = 10$ and $d = 50$ . Find $P ( x > 50 )$ .

Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$ . Find the probability that $x$ will assume a value within the interval $\mu \pm 2 \sigma$ .

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 12$ . Find the $z$ -score that corresponds to the value $x = 72$ .

$\text { Compute } \left( \begin{array} { l } 4 \\4\end{array} \right)$

Suppose $x$ is a uniform random variable with $c = 10$ and $d = 80$ . Find the mean of the random variable $x$ .

Suppose that x has an exponential distribution with $\theta = 2 \text {. Find } P ( x < 1.5 ) \text {. }$

Suppose that x has an exponential distribution with $\theta = 1.5 . \text { Find } P ( x > 1 )$

Assume that $x$ is a binomial random variable with $\mathrm { n } = 400$ and $\mathrm { p } = 0.30$ . Use a normal approximation to find $P ( x \geq 100 )$ .

Determine the value of $e ^ { - a / \theta }$ for $\theta = 2$ and $a = 3$ .

For a standard normal random variable, find the probability that z exceeds the value $- 1.65$