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Exam 7: Continuous Probability Distributions

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Question 51

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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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95.5% and ...

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Question 52

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The exponential distribution is a family of discrete distributions,all of which are negatively skewed.

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Question 53

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In 2000,the average charge of tax preparation was $95.Assuming a normal distribution and a standard deviation of $10,use the approximate areas beneath the normal curve,as discussed in this section,to answer: What proportion of tax preparation fees were more than $115?

Grades for a statistics exam for a certain class follow the normal probability distribution with a mean of 82 and a standard deviation of 12.What percentage of the students in the class had a grade 81 or more?

If Excel and Minitab packages are both used to generate its own sample of 10,000 observations from a theoretical continuous distribution,the two sets of observations are expected to be identical.

The proportion of the data from a standard normal distribution that falls within two standard deviations from the mean is:

The standard deviation of the binomial distribution with n = 25 and $\pi$ = .50 is 6.25.

In the normal distribution,the total area under the curve is equal to ____________________.

Let z₁ be a z score that is unknown but identifiable by position and area.If the area to the right of z₁ is 0.8413,then the value of z₁ must be:

The age of customers for a particular retail store follows a normal distribution with a mean of 37.5 years and a standard deviation of 7.6 years.What is the probability that the next customer who enters the store will be less than 42 years old?

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

Regardless of the shape of a particular normal curve,about 75% of the area is within the interval $\mu \pm \sigma$ ,where $\mu$ and $\text { ? }$ are the mean and the standard deviation,respectively.

Which of the following is not a characteristic for a normal distribution?

If x is a normal random variable with a mean of 100 and a standard deviation of 10,find the following probabilities: A)P(x ≥ 128) B)P(x ≤ 113) C)P(87 ≤ x ≤ 98)

An elementary school teacher learned that 40 percent of school age children have at least 3 cavities.The teacher has 30 students in his class.What is the standard deviation for the number of school age children that have at least 3 cavities?

The z-score representing the 90th percentile of the standard normal distribution is:

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

A manufacturer of washing machines has experienced a 2% repair rate.In a city where 120,000 of its machines are located,the company plans to open its own repair service and needs to determine the number of repair workers to hire.Each worker can handle calls for 1000 machine repairs.If the company wants to cover calls 90% of the time,how many workers must it hire for the new repair facility?

For a normal curve,if the mean is 20 minutes and the standard deviation is 5 minutes,find the area to the right of 12 minutes.

In a paper mill,which produces newsprint from Southern Pine,the production manager finds a flaw for each 1000 feet of newsprint.He knows that the outcome is a Poisson process with a continuous distribution.If x = feet between flaws,what is the probability of finding 600 or more feet between the next two flaws?