Calculate the mean for the discrete probability distribution shown here. \[\begin{array} { l | c c c c } X & 3 & 4 & 8 & 11 \\ \hline P ( X ) & 0.26 & 0.1 & 0.06 & 0.58 \end{array}\]

A) 26 B) 8.04 C) 6.5 D) 2.01 A) 26 B) 8.04 C) 6.5 D) 2.01

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

A) .2 B) .7 C) .5 D) .3 A) .2 B) .7 C) .5 D) .3

Exam 4: Random Variables and Probability Distributions

A coin is flipped 6 times. The variable x represents the number of tails obtained. List the possible values $\text { of } x . \operatorname { Is } x$ discrete or continuous? Explain.

Free

(Essay)

4.7/5

(36)

Question 1

Correct Answer:

Verified

possible values of $\text { of } x : \{ 0,1,2,3,4,5,6 \} \text {; The variable } x$ is discrete since it has a finite number of distinct possible values.

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 less than 1 year.

Free

(Multiple Choice)

4.9/5

(36)

Question 2

Correct Answer:

Verified

C

About 40% of the general population donate time and energy to community projects. suppose 15 people have been randomly selected from a community and each asked whether he or she donates time and energy to community projects. Let x be the number who donate time and energy to community projects. Use a binomial probability table to find the probability that more than five of the 15 donate time and energy to community projects.

Free

(Essay)

5.0/5

(33)

Question 3

Correct Answer:

Verified

$X$ is a binomial random variable with $n = 15$ and $p = 0.4$ .
$\begin{aligned}P ( x > 5 ) = 1 - \mathrm { P } ( x \leq 5 ) & = 1 - 0.403 \text { (from a binomial probability table) } \\& = 0.597\end{aligned}$

The binomial distribution can be used to model the number of rare events that occur over a given time period.

(True/False)

4.8/5

(35)

Question 4

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 9$ . Find the $\mathrm { z }$ -score that corresponds to the value $x = 96$ .

(Multiple Choice)

4.9/5

(39)

Question 5

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 standard deviation of this distribution.

(Multiple Choice)

4.9/5

(43)

Question 6

After a particular heavy snowstorm, the depth of snow reported in a mountain village followed a uniform distribution over the interval from 15 to 22 inches of snow. Find the probability that a randomly selected location in this village had between 17 and 18 inches of snow. Round to the nearest ten-thousandth.

(Multiple Choice)

4.9/5

(30)

Question 7

The random variable x represents the number of boys in a family with three children. Assuming that births of boys and girls are equally likely, find the mean and standard deviation for the random variable x.

(Multiple Choice)

4.9/5

(36)

Question 8

Calculate the mean for the discrete probability distribution shown here. X 3 4 8 11 P(X) 0.26 0.1 0.06 0.58

(Multiple Choice)

4.8/5

(30)

Question 9

If x is a binomial random variable, calculate µ for n = 30 and p = 0.7.

(Multiple Choice)

4.7/5

(39)

Question 10

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 two accidents will occur on this stretch of road during a month.

(Essay)

4.7/5

(38)

Question 11

Consider the given discrete probability distribution. Find $P ( x > 3 )$ x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

(Multiple Choice)

4.9/5

(36)

Question 12

Consider the given discrete probability distribution. Construct a graph for $p ( x )$ x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

(Essay)

4.8/5

(41)

Question 13

The time between arrivals at an ATM machine follows an exponential distribution with $\theta = 10$ minutes. Find the mean and standard deviation of this distribution.

(Multiple Choice)

4.8/5

(37)

Question 14

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

(Essay)

4.8/5

(45)

Question 15

The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 6. Find the probability that exactly three road construction projects are currently taking place in this city.

(Multiple Choice)

4.8/5

(34)

Question 16

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 61°F to 91°F. Find the temperature which is exceeded by the high temperatures on 90% of the days in August.

(Multiple Choice)

4.8/5

(37)

Question 17

Which of the following is not a method used for determining whether data are from an approximately normal distribution?

(Multiple Choice)

4.9/5

(37)

Question 18

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 75°F to 95°F. What is the probability that a random day in August has a high temperature that exceeds 80°F?

(Essay)

4.8/5

(30)

Question 19

Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions.

(Multiple Choice)

4.8/5

(39)

Question 20

A coin is flipped 6 times. The variable x represents the number of tails obtained. List the possible values $\text { of } x . \operatorname { Is } x$ discrete or continuous? Explain.

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 less than 1 year.

The binomial distribution can be used to model the number of rare events that occur over a given time period.

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 9$ . Find the $\mathrm { z }$ -score that corresponds to the value $x = 96$ .

The random variable x represents the number of boys in a family with three children. Assuming that births of boys and girls are equally likely, find the mean and standard deviation for the random variable x.

Calculate the mean for the discrete probability distribution shown here. X 3 4 8 11 P(X) 0.26 0.1 0.06 0.58

If x is a binomial random variable, calculate µ for n = 30 and p = 0.7.

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 two accidents will occur on this stretch of road during a month.

Consider the given discrete probability distribution. Find $P ( x > 3 )$ x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

Consider the given discrete probability distribution. Construct a graph for $p ( x )$ x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

The time between arrivals at an ATM machine follows an exponential distribution with $\theta = 10$ minutes. Find the mean and standard deviation of this distribution.

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 6. Find the probability that exactly three road construction projects are currently taking place in this city.

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 61°F to 91°F. Find the temperature which is exceeded by the high temperatures on 90% of the days in August.

Which of the following is not a method used for determining whether data are from an approximately normal distribution?

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 75°F to 95°F. What is the probability that a random day in August has a high temperature that exceeds 80°F?

Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions.

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

A coin is flipped 6 times. The variable x represents the number of tails obtained. List the possible values of x.Is⁡x\text { of } x . \operatorname { Is } x of x.Isx discrete or continuous? Explain.

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 less than 1 year.

The binomial distribution can be used to model the number of rare events that occur over a given time period.

Suppose a random variable xxx is best described by a normal distribution with μ=60\mu = 60μ=60 and σ=9\sigma = 9σ=9 . Find the z\mathrm { z }z -score that corresponds to the value x=96x = 96x=96 .

The random variable x represents the number of boys in a family with three children. Assuming that births of boys and girls are equally likely, find the mean and standard deviation for the random variable x.

Calculate the mean for the discrete probability distribution shown here. X 3 4 8 11 P(X) 0.26 0.1 0.06 0.58

If x is a binomial random variable, calculate µ for n = 30 and p = 0.7.

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 two accidents will occur on this stretch of road during a month.

Consider the given discrete probability distribution. Find P(x>3)P ( x > 3 )P(x>3) x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

Consider the given discrete probability distribution. Construct a graph for p(x)p ( x )p(x) x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

The time between arrivals at an ATM machine follows an exponential distribution with θ=10\theta = 10θ=10 minutes. Find the mean and standard deviation of this distribution.

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 6. Find the probability that exactly three road construction projects are currently taking place in this city.

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 61°F to 91°F. Find the temperature which is exceeded by the high temperatures on 90% of the days in August.

Which of the following is not a method used for determining whether data are from an approximately normal distribution?

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 75°F to 95°F. What is the probability that a random day in August has a high temperature that exceeds 80°F?

Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions.

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

A coin is flipped 6 times. The variable x represents the number of tails obtained. List the possible values $\text { of } x . \operatorname { Is } x$ discrete or continuous? Explain.

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 9$ . Find the $\mathrm { z }$ -score that corresponds to the value $x = 96$ .

Consider the given discrete probability distribution. Find $P ( x > 3 )$ x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

Consider the given discrete probability distribution. Construct a graph for $p ( x )$ x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

The time between arrivals at an ATM machine follows an exponential distribution with $\theta = 10$ minutes. Find the mean and standard deviation of this distribution.