Exam 4: Random Variables and Probability Distributions

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability that the random variable x is a value greater than 5. 2 3 5 8 10 () 0.10 0.20 0.30 0.30 0.10

(Multiple Choice)

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Question 21

A dice game involves rolling three dice and betting on one of the six numbers that are on the dice. The game costs $7 to play, and you win if the number you bet appears on any of the dice. The distribution for the outcomes of the game (including the profit) is shown below: Number of dice with your number Profit Probability 0 -\ 7 125/216 1 \ 7 75/216 2 \ 9 15/216 3 \ 21 1/216 Find your expected profit from playing this game.

(Multiple Choice)

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Question 22

Data has been collected and a normal probability plot for one of the variables is shown below. Based on your knowledge of normal probability plots, do you believe the variable in question is normally distributed? The data are represented by the"o" symbols in the plot.

(Multiple Choice)

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Question 23

The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce. The company receives complaints from consumers who actually measure the amount of soda in the cans and claim that the volume is less than the advertised 12 ounces. What proportion of the soda cans Contain less than the advertised 12 ounces of soda?

(Multiple Choice)

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Question 24

Given that $x$ is a hypergeometric random variable with $N = 10 , n = 3$ , and $r = 5$ : a. Display the probability distribution in tabular form. b. Compute $\mu$ and $\sigma$ for $x$ . c. What is the probability that $x$ will fall within the interval $\mu \pm 2 \sigma$

(Essay)

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Question 25

The age of customers at a local hardware store follows a uniform distribution over the interval from 18 to 60 years old. Find the average age of customers to this hardware store.

(Multiple Choice)

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Question 26

Which binomial probability is represented on the screen below?

(Multiple Choice)

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Question 27

$\text { Find a value of the standard normal random variable } z \text {, called } z _ { 0 } \text {, such that } P \left( - z _ { 0 } \leq z \leq z _ { 0 } \right) = 0.98 \text {. }$

(Multiple Choice)

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Question 28

A recent survey found that 61% of all adults over 50 wear glasses for driving. In a random sample of 70 adults over 50, what is the mean and standard deviation of the number who wear glasses? round to the nearest hundredth when necessary.

(Multiple Choice)

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Question 29

Assume that $x$ is a binomial random variable with $\mathrm { n } = 1000$ and $\mathrm { p } = 0.80$ . Use a normal approximation to find $\mathrm { P } ( 800 < \mathrm { x } \leq 825 )$ .

(Multiple Choice)

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Question 30

We believe that 90% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 23 students from the population and observed fewer than five in our sample who consider statistics to be an exciting subject. Make an inference about the belief that 90% of the students consider statistics to be an exciting subject.

(Multiple Choice)

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Question 31

The total area under a probability distribution equals 1.

(True/False)

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Question 32

Classify the following random variable according to whether it is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska

(Multiple Choice)

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Question 33

For any continuous probability distribution, $P ( x = c ) = 0 \text { for all values of } c \text {. }$

(True/False)

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Question 34

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with $\lambda = 4.6$ alarms per year. Find the probability that a randomly selected customer had more than 7 alarms reported.

(Multiple Choice)

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Question 35

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 8.5. Interpret the value of the mean.

(Multiple Choice)

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Question 36

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 16$ . Find the $z$ -score that corresponds to the value $x = 0$ .

(Multiple Choice)

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Question 37

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. Find the approximate probability that more than 30 of the sampled students had at least one tattoo.

(Multiple Choice)

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Question 38

Suppose x is a random variable for which a Poisson probability distribution with $\lambda = 3$ 3 provides a good approximation. a. Graph $p ( x )$ for $x = 0,1,2,3,4,5,6$ . b. Find $\mu$ and $\sigma$ for $x$ . c. What is the probability that $x$ will fall in the interval $\mu \pm \sigma$ ?

(Essay)

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Question 39

Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

(Multiple Choice)

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Question 40

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability that the random variable x is a value greater than 5. 2 3 5 8 10 () 0.10 0.20 0.30 0.30 0.10

Data has been collected and a normal probability plot for one of the variables is shown below. Based on your knowledge of normal probability plots, do you believe the variable in question is normally distributed? The data are represented by the"o" symbols in the plot.

Given that $x$ is a hypergeometric random variable with $N = 10 , n = 3$ , and $r = 5$ : a. Display the probability distribution in tabular form. b. Compute $\mu$ and $\sigma$ for $x$ . c. What is the probability that $x$ will fall within the interval $\mu \pm 2 \sigma$

The age of customers at a local hardware store follows a uniform distribution over the interval from 18 to 60 years old. Find the average age of customers to this hardware store.

Which binomial probability is represented on the screen below?

$\text { Find a value of the standard normal random variable } z \text {, called } z _ { 0 } \text {, such that } P \left( - z _ { 0 } \leq z \leq z _ { 0 } \right) = 0.98 \text {. }$

A recent survey found that 61% of all adults over 50 wear glasses for driving. In a random sample of 70 adults over 50, what is the mean and standard deviation of the number who wear glasses? round to the nearest hundredth when necessary.

Assume that $x$ is a binomial random variable with $\mathrm { n } = 1000$ and $\mathrm { p } = 0.80$ . Use a normal approximation to find $\mathrm { P } ( 800 < \mathrm { x } \leq 825 )$ .

The total area under a probability distribution equals 1.

Classify the following random variable according to whether it is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska

For any continuous probability distribution, $P ( x = c ) = 0 \text { for all values of } c \text {. }$

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with $\lambda = 4.6$ alarms per year. Find the probability that a randomly selected customer had more than 7 alarms reported.

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 8.5. Interpret the value of the mean.

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 16$ . Find the $z$ -score that corresponds to the value $x = 0$ .

Suppose x is a random variable for which a Poisson probability distribution with $\lambda = 3$ 3 provides a good approximation. a. Graph $p ( x )$ for $x = 0,1,2,3,4,5,6$ . b. Find $\mu$ and $\sigma$ for $x$ . c. What is the probability that $x$ will fall in the interval $\mu \pm \sigma$ ?

Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

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

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Exam 4: Random Variables and Probability Distributions

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability that the random variable x is a value greater than 5. 2 3 5 8 10 () 0.10 0.20 0.30 0.30 0.10

Data has been collected and a normal probability plot for one of the variables is shown below. Based on your knowledge of normal probability plots, do you believe the variable in question is normally distributed? The data are represented by the"o" symbols in the plot.

The age of customers at a local hardware store follows a uniform distribution over the interval from 18 to 60 years old. Find the average age of customers to this hardware store.

Which binomial probability is represented on the screen below?

A recent survey found that 61% of all adults over 50 wear glasses for driving. In a random sample of 70 adults over 50, what is the mean and standard deviation of the number who wear glasses? round to the nearest hundredth when necessary.

Assume that xxx is a binomial random variable with n=1000\mathrm { n } = 1000n=1000 and p=0.80\mathrm { p } = 0.80p=0.80 . Use a normal approximation to find P(800<x≤825)\mathrm { P } ( 800 < \mathrm { x } \leq 825 )P(800<x≤825) .

The total area under a probability distribution equals 1.

Classify the following random variable according to whether it is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska

For any continuous probability distribution, P(x=c)=0 for all values of c. P ( x = c ) = 0 \text { for all values of } c \text {. }P(x=c)=0 for all values of c.

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with λ=4.6\lambda = 4.6λ=4.6 alarms per year. Find the probability that a randomly selected customer had more than 7 alarms reported.

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 8.5. Interpret the value of the mean.

Suppose a random variable xxx is best described by a normal distribution with μ=60\mu = 60μ=60 and σ=16\sigma = 16σ=16 . Find the zzz -score that corresponds to the value x=0x = 0x=0 .

Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

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

Assume that $x$ is a binomial random variable with $\mathrm { n } = 1000$ and $\mathrm { p } = 0.80$ . Use a normal approximation to find $\mathrm { P } ( 800 < \mathrm { x } \leq 825 )$ .

For any continuous probability distribution, $P ( x = c ) = 0 \text { for all values of } c \text {. }$

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with $\lambda = 4.6$ alarms per year. Find the probability that a randomly selected customer had more than 7 alarms reported.

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 16$ . Find the $z$ -score that corresponds to the value $x = 0$ .