Question 1

Although the binomial distribution is discrete and the normal distribution is continuous,the normal distribution is a good approximation to the binomial whenever both ____________________ and ____________________ are ≥ 5,where n = number of trials,and $\pi$ = the probability of success in any given trial,are the parameters of the binomial distribution.

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Question 2

Scores of high school students on a national mathematics exam in Egypt were normally distributed with a mean of 86 and a standard deviation of 4.
A)What is the probability that a randomly selected student will have a score of 80 or higher?
B)If there were 97,680 students with scores higher than 91,how many students took the test?
____________________ (Remove all commas from your answer before submitting).

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Question 3

Explain what we mean by saying a random variable is approximately normally distributed.

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Question 4

Why is it important to use the correction for continuity when approximating binomial probabilities with the normal distribution?

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Question 5

Use the properties of the standard normal curve to describe the method of finding the area to the right of z = 1.42.

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Question 6

The normal distribution is a very good approximation to the binomial distribution whenever ____________________ and ____________________ are ≥ 5.

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Question 7

A continuous random variable x has the following probability density function: f(x)= 2e^-2^x,x ≥ 0 What is the distribution of the random variable x?

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Question 8

Express in your own words the procedure for finding the area under the standard normal curve between z = 0 and z = 1.53.

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Question 9

Why is the probability that a continuous random variable takes on any specific value equal to zero?

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Question 10

The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes.What is the probability density function for the time it takes a technician to fix a computer problem?

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Question 11

Describe the method of finding the area under the standard normal curve between z = 0 and z =- 1.33.

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Question 12

A certain brand of flood lamps has a lifetime that is normally distributed with a mean of 3,750 hours and a standard deviation of 300 hours.
A)What proportion of these lamps will last for more than 4,000 hours?
B)What lifetime should the manufacturer advertise for these lamps in order that only 2% of the lamps will burn out before the advertised lifetime?
____________________ hours (Remove all commas from your answer before submitting).

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Question 13

Regardless of the shape of a particular normal curve,about what percentage of the area is within $\mu \pm 3\sigma$,respectively,where $\mu$is the mean and $\sigma$ is the standard deviation.

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Question 14

Complete the following table indicating which procedure to use in calculating binomial probabilities:
 $$\begin{array} { | c | c | c | } 
\hline n & \pi & \text { Procedure } \
\hline \text { Large } & 0 .2 \leq \pi \leq 0 . 8 & \
\hline \text { Large } & 0 .0 \leq \pi \leq 0.1 & \
\hline \text { Large } & 0.9 \leq \pi \leq 1.0 & \
\hline \text { Small } & 0 .0 \leq \pi \leq 1.0 & \
\hline
\end{array}$$

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Question 15

Explain why the total area beneath a probability density function is equal to 1.0.

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Question 16

What does it mean when we say a random variable is standardized?

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Question 17

Identify the distribution shown in the following graph.Indicate the approximate areas that will lie beneath the curve for the intervals shown.

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Question 18

What are the mean and standard deviation of a normally distributed random variable,which has been "standardized"?
Mean = ____________________
SD = ____________________

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Question 19

What are continuous probability distributions?

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Question 20

For a value of z = -1.59,explain the steps needed to find the area to the left of this value.

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Quiz 7: Continuous Probability Distributions

Explain what we mean by saying a random variable is approximately normally distributed.

Why is it important to use the correction for continuity when approximating binomial probabilities with the normal distribution?

Use the properties of the standard normal curve to describe the method of finding the area to the right of z = 1.42.

The normal distribution is a very good approximation to the binomial distribution whenever and are ≥ 5.

A continuous random variable x has the following probability density function: f(x)= 2e^-2^x,x ≥ 0 What is the distribution of the random variable x?

Express in your own words the procedure for finding the area under the standard normal curve between z = 0 and z = 1.53.

Why is the probability that a continuous random variable takes on any specific value equal to zero?

The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes.What is the probability density function for the time it takes a technician to fix a computer problem?

Describe the method of finding the area under the standard normal curve between z = 0 and z =- 1.33.

Regardless of the shape of a particular normal curve,about what percentage of the area is within $\mu \pm 3\sigma$ ,respectively,where $\mu$ is the mean and $\sigma$ is the standard deviation.

Explain why the total area beneath a probability density function is equal to 1.0.

What does it mean when we say a random variable is standardized?

Identify the distribution shown in the following graph.Indicate the approximate areas that will lie beneath the curve for the intervals shown.

What are the mean and standard deviation of a normally distributed random variable,which has been "standardized"? Mean = SD =

What are continuous probability distributions?

For a value of z = -1.59,explain the steps needed to find the area to the left of this value.

Quiz 7: Continuous Probability Distributions

Explain what we mean by saying a random variable is approximately normally distributed.

Why is it important to use the correction for continuity when approximating binomial probabilities with the normal distribution?

Use the properties of the standard normal curve to describe the method of finding the area to the right of z = 1.42.

The normal distribution is a very good approximation to the binomial distribution whenever ____________________ and ____________________ are ≥ 5.

A continuous random variable x has the following probability density function: f(x)= 2e-2x ,x ≥ 0 What is the distribution of the random variable x?

Express in your own words the procedure for finding the area under the standard normal curve between z = 0 and z = 1.53.

Why is the probability that a continuous random variable takes on any specific value equal to zero?

The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes.What is the probability density function for the time it takes a technician to fix a computer problem?

Describe the method of finding the area under the standard normal curve between z = 0 and z =- 1.33.

Regardless of the shape of a particular normal curve,about what percentage of the area is within μ±3σ\mu \pm 3\sigmaμ±3σ ,respectively,where μ\muμ is the mean and σ\sigmaσ is the standard deviation.

Explain why the total area beneath a probability density function is equal to 1.0.

What does it mean when we say a random variable is standardized?

Identify the distribution shown in the following graph.Indicate the approximate areas that will lie beneath the curve for the intervals shown.

What are the mean and standard deviation of a normally distributed random variable,which has been "standardized"? Mean = ____________________ SD = ____________________

What are continuous probability distributions?

For a value of z = -1.59,explain the steps needed to find the area to the left of this value.

The normal distribution is a very good approximation to the binomial distribution whenever and are ≥ 5.

A continuous random variable x has the following probability density function: f(x)= 2e^-2^x,x ≥ 0 What is the distribution of the random variable x?

Regardless of the shape of a particular normal curve,about what percentage of the area is within $\mu \pm 3\sigma$ ,respectively,where $\mu$ is the mean and $\sigma$ is the standard deviation.

What are the mean and standard deviation of a normally distributed random variable,which has been "standardized"? Mean = SD =