A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below: \[\begin{array} { l | c c c } \text { Price } & \$ 10.00 & \$ 12.50 & \$ 15.00 \\ \hline \text { Probability } & 0.3 & 0.45 & 0.25 \end{array}\] Suppose the mean cost of the frogs is $12.38 per week. Interpret this value.

A) The average cost for all weekly frog purchases is $12.38. B) The frog cost that occurs more often than any other is $12.38. C) The median cost for the distribution of frog costs is $12.38. D) Most of the weeks resulted in frog costs of $12.38. A) The average cost for all weekly frog purchases is $12.38. B) The frog cost that occurs more often than any other is $12.38. C) The median cost for the distribution of frog costs is $12.38. D) Most of the weeks resulted in frog costs of $12.38.

Exam 4: Random Variables and Probability Distributions

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 mean and standard deviation for this binomial distribution.

(Multiple Choice)

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Question 161

$\text { Given that } x \text { is a hypergeometric random variable, compute } p ( x ) \text { for } N = 8 , n = 5 , r = 3 \text {, and } x = 2 \text {. }$

(Multiple Choice)

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Question 162

Which of the following statements is not a property of the normal curve?

(Multiple Choice)

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Question 163

The conditions for both the hypergeometric and the binomial random variables require that each trial results in one of two outcomes.

(True/False)

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Question 164

$\text { Compute } \frac { \lambda ^ { x } e ^ { - \lambda } } { x ! } \text { for } \lambda = 5 \text { and } x = 7$

(Essay)

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Question 165

Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 3. Find the probability that exactly six babies are born during a randomly selected hour.

(Essay)

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Question 166

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 42% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled. Assuming the paper's claim is correct, find the probability that more than eight but fewer than 12 of the 20 sampled believe the company's president possesses low ethical standards. Round to six decimal places.

(Multiple Choice)

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Question 167

The time between arrivals at an ATM machine follows an exponential distribution with $\theta = 10$ minutes. Find the probability that less than 25 minutes will pass between arrivals.

(Multiple Choice)

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Question 168

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 5$ and $d = 9$ . Find the value of a that makes the following probability statement true: $P ( x \leq a ) = 0.6$ .

(Multiple Choice)

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Question 169

Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 7. Find the probability that exactly two babies will be born during a particular 1-hour period at this hospital.

(Multiple Choice)

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Question 170

Find the mean and standard deviation of the probability distribution for the random variable x, which represents the number of cars per household in a small town. x P(x) 0 .125 1 .428 2 .256 3 .108 4 .083

(Essay)

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Question 171

The continuity correction factor is the name given to the .5 adjustment necessary when estimating the binomial with the normal distribution.

(True/False)

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Question 172

The exponential distribution is governed by two quantities, $\mu \text { and } c$ , that determine its shape and location

(True/False)

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Question 173

The following data represent the scores of a sample of 50 students on a statistics exam. The mean score is $\bar { x } = 80.3 \text {, and the standard deviation is } s = 11.37$ 49 51 59 63 66 68 68 69 70 71 71 71 73 74 76 76 76 77 78 79 79 79 79 80 80 82 83 83 83 85 85 86 86 88 88 88 88 89 89 89 90 91 92 92 93 95 96 97 97 98 What percentage of the scores fall in each of the intervals $\bar { x } \pm s , \bar { x } \pm 2 s$ , and $\bar { x } \pm 3 s$ ? Based on these percentages, do you believe that the distribution of scores is approximately normal? Explain.

(Essay)

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Question 174

Which geometric shape is used to represent areas for a uniform distribution?

(Multiple Choice)

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Question 175

If x is a binomial random variable, calculate σ f $n = 100 \text { and } p = 0.2$ . Round to three decimal places when necessary.

(Multiple Choice)

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Question 176

A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below: Price \ 10.00 \ 12.50 \ 15.00 Probability 0.3 0.45 0.25 Suppose the mean cost of the frogs is $12.38 per week. Interpret this value.

(Multiple Choice)

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Question 177

Suppose that 67% of the employees of a company participate in the company's medical savings program. Let x be the number of employees who participate in the program in a random sample of 50 employees. Find the mean and standard deviation of $x$

(Essay)

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Question 178

The school newspaper surveyed 100 commuter students and asked two questions. First, students were asked how many courses they were currently enrolled in. Second, the commuter students were asked to estimate how long it took them to drive to campus. Considering these two variables, number of courses would best be considered a _ variable and drive time would be Considered a _ variable.

(Multiple Choice)

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Question 179

The exponential distribution is sometimes called the waiting-time distribution, because it is used to describe the length of time between occurrences of random events.

(True/False)

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Question 180

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 mean and standard deviation for this binomial distribution.

$\text { Given that } x \text { is a hypergeometric random variable, compute } p ( x ) \text { for } N = 8 , n = 5 , r = 3 \text {, and } x = 2 \text {. }$

Which of the following statements is not a property of the normal curve?

The conditions for both the hypergeometric and the binomial random variables require that each trial results in one of two outcomes.

$\text { Compute } \frac { \lambda ^ { x } e ^ { - \lambda } } { x ! } \text { for } \lambda = 5 \text { and } x = 7$

Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 3. Find the probability that exactly six babies are born during a randomly selected hour.

The time between arrivals at an ATM machine follows an exponential distribution with $\theta = 10$ minutes. Find the probability that less than 25 minutes will pass between arrivals.

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 5$ and $d = 9$ . Find the value of a that makes the following probability statement true: $P ( x \leq a ) = 0.6$ .

Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 7. Find the probability that exactly two babies will be born during a particular 1-hour period at this hospital.

Find the mean and standard deviation of the probability distribution for the random variable x, which represents the number of cars per household in a small town. x P(x) 0 .125 1 .428 2 .256 3 .108 4 .083

The continuity correction factor is the name given to the .5 adjustment necessary when estimating the binomial with the normal distribution.

The exponential distribution is governed by two quantities, $\mu \text { and } c$ , that determine its shape and location

Which geometric shape is used to represent areas for a uniform distribution?

If x is a binomial random variable, calculate σ f $n = 100 \text { and } p = 0.2$ . Round to three decimal places when necessary.

A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below: Price \ 10.00 \ 12.50 \ 15.00 Probability 0.3 0.45 0.25 Suppose the mean cost of the frogs is $12.38 per week. Interpret this value.

Suppose that 67% of the employees of a company participate in the company's medical savings program. Let x be the number of employees who participate in the program in a random sample of 50 employees. Find the mean and standard deviation of $x$

The exponential distribution is sometimes called the waiting-time distribution, because it is used to describe the length of time between occurrences of random events.

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 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 mean and standard deviation for this binomial distribution.

Which of the following statements is not a property of the normal curve?

The conditions for both the hypergeometric and the binomial random variables require that each trial results in one of two outcomes.

Compute λxe−λx! for λ=5 and x=7\text { Compute } \frac { \lambda ^ { x } e ^ { - \lambda } } { x ! } \text { for } \lambda = 5 \text { and } x = 7 Compute x!λxe−λ​ for λ=5 and x=7

Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 3. Find the probability that exactly six babies are born during a randomly selected hour.

The time between arrivals at an ATM machine follows an exponential distribution with θ=10\theta = 10θ=10 minutes. Find the probability that less than 25 minutes will pass between arrivals.

Suppose xxx is a random variable best described by a uniform probability distribution with c=5c = 5c=5 and d=9d = 9d=9 . Find the value of a that makes the following probability statement true: P(x≤a)=0.6P ( x \leq a ) = 0.6P(x≤a)=0.6 .

Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 7. Find the probability that exactly two babies will be born during a particular 1-hour period at this hospital.

Find the mean and standard deviation of the probability distribution for the random variable x, which represents the number of cars per household in a small town. x P(x) 0 .125 1 .428 2 .256 3 .108 4 .083

The continuity correction factor is the name given to the .5 adjustment necessary when estimating the binomial with the normal distribution.

The exponential distribution is governed by two quantities, μ and c\mu \text { and } cμ and c , that determine its shape and location

Which geometric shape is used to represent areas for a uniform distribution?

If x is a binomial random variable, calculate σ f n=100 and p=0.2n = 100 \text { and } p = 0.2n=100 and p=0.2 . Round to three decimal places when necessary.

A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below: Price \ 10.00 \ 12.50 \ 15.00 Probability 0.3 0.45 0.25 Suppose the mean cost of the frogs is $12.38 per week. Interpret this value.

Suppose that 67% of the employees of a company participate in the company's medical savings program. Let x be the number of employees who participate in the program in a random sample of 50 employees. Find the mean and standard deviation of xxx

The exponential distribution is sometimes called the waiting-time distribution, because it is used to describe the length of time between occurrences of random events.

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

$\text { Compute } \frac { \lambda ^ { x } e ^ { - \lambda } } { x ! } \text { for } \lambda = 5 \text { and } x = 7$

The time between arrivals at an ATM machine follows an exponential distribution with $\theta = 10$ minutes. Find the probability that less than 25 minutes will pass between arrivals.

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 5$ and $d = 9$ . Find the value of a that makes the following probability statement true: $P ( x \leq a ) = 0.6$ .

The exponential distribution is governed by two quantities, $\mu \text { and } c$ , that determine its shape and location

If x is a binomial random variable, calculate σ f $n = 100 \text { and } p = 0.2$ . Round to three decimal places when necessary.

Suppose that 67% of the employees of a company participate in the company's medical savings program. Let x be the number of employees who participate in the program in a random sample of 50 employees. Find the mean and standard deviation of $x$