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Exam 6: The Normal Probability Distribution

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Question 1

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Even though the normal probability distribution deals with continuous variables, under certain circumstances, we can use it to approximate various discrete probability distributions. Such use of the normal probability distribution is permissible:

A) in the case of binomial probabilities, when np > 5 and also nq > 5
B) in the case of Poisson probabilities, when> 100
C) in the case of hypergeometric probabilities, when np > 1 and also n1 > 1
D) in all of these
E) in none of these

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Question 2

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If the random variable x is normally distributed with a mean of 88 and a standard deviation of 12, then P(X 96) is:

A) 0.2486
B) 0.2514
C) 0.1243
D) 0.4972
E) 0.3398

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Question 3

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The annual rainfall in a particular area of the country is normally distributed with mean 40 inches and standard deviation 8 inches. In what proportion of years will the annual rainfall be between 42 and 50 inches? ______________ A drought occurs after a year where the annual rainfall was below the 20th percentile. Find the 20th percentile for the annual rainfall in this area of the country. ______________

The admissions office of a community college in Indiana is asked to accept deposits from a number of qualified prospective freshmen so that, with probability about 0.95, the size of the freshmen class will be less than or equal to 150. Suppose the applicants constitute a random sample from a population of applicants, 80% of whom would actually enter the freshmen class if accepted. How many deposits should the admissions counselor accept? ______________ If applicants in the number determined in part (a) are accepted, what is the probability that the freshmen class size will be less than 135? ______________

Given that z is a standard normal variable, the value for which P( ) = 0.242 is:

Which of the following correctly describes the normal probability distribution?

Members of the normal probability distribution family differ from one another only by:

If the standard normal deviate of a random variable value of x = 2 is z = -2, while the standard deviation of the random variable x equals 2, then the mean of x is:

A firm with many traveling salespersons decides to check the salespersons' travel expenses to see if they are correctly reported. An auditor for the firm selects 200 expense reports at random to audit. What is the probability more than 20% of the sampled reports will be incorrect when, in fact, only 10% of the firm's expense reports are improperly documented? ______________

For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, the area to the right of 13 minutes is 0.9192.

The total area under the normal probability distribution curve is equal to 1.

Which of the following is always true for all probability density functions of continuous random variables?

A manufacturer of bike racks for cars claims that the assembly time x for a particular model is normally distributed with a mean of 1 hour and a standard deviation of 0.10 hours. Find the probability that it takes at most 1.1 hours to assemble a bike rack of this model. ______________ Find the probability that it takes longer than 1.2 hours to assemble a bike rack of this model. ______________ Find the probability that it takes between 0.8 hours and 1.1 hours to assemble a bike rack of this model. ______________ Find the assembly time that exceeds 97.5% of all other assembly times for bike racks of this model. ______________

In general, the binomial probability P(X x) is approximated by the area under the normal curve to the left of x + - .5.

What proportion of the data from a normal distribution is within two standard deviations from the mean?

The mean, median, and standard deviation of a normally distributed random variable are all at the same position on the horizontal axis since the distribution is symmetric.

Suppose z has a standard normal distribution. Then 95.96% of the possible z values are between ______________ and ______________ (symmetrically distributed around the mean).

The proportion of the total area under the normal curve that lies within one standard deviation of the mean is approximately 0.75.

If X is a normal random variable with a mean of 45 and a standard deviation of 8, find the following probabilities: a. P(X 50) ______________ b. P(X 32) ______________ c. P(37 X 48) ______________ d. P(50 X 60) ______________ e. P(X = 45) ______________

If x is a normal random variable with mean of 1228 and a standard deviation of 120, the number of standard deviations from 1228 to 1380 is: