Exam 7: Continuous Probability Distributions

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The standard normal distribution has a mean of 0.0 and standard deviation of 1.0.

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Find z1 if the area to the left of a positive z1 is 0.9131.

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If the mean of an exponential distribution is 2,then the value of the parameter λ\lambda is:

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Given that z is a standard normal random variable,a negative value of z indicates that:

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The time it takes a technician to fix a computer problem is exponentially distributed with a mean of 15 minutes.What is the probability that it will take a technician less than 10 minutes to fix a computer problem?

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Assume x is normally distributed with mean μ\mu = 15 and standard deviation  σ \text { σ } = 3.Use the approximate areas beneath the normal curve,as discussed in this section,to find P(x = 20).

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The selling price of various homes in a community follows the normal distribution with a mean of $176,000 and a standard deviation of $22,300.What is the probability that the next house will sell for between $150,000 and $168,000?

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Complete the following table indicating which procedure to use in calculating binomial probabilities: n \pi Procedure Large 0.2\leq\pi\leq0.8 Large 0.0\leq\pi\leq0.1 Large 0.9\leq\pi\leq1.0 Small 0.0\leq\pi\leq1.0

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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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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 between $80 and $90?

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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 between $75 and $115?

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Which of the following statements are true regarding the normal distribution curve?

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For the standard normal curve,determine the area to the right of z = 0.34.

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Assume x is normally distributed with mean μ\mu = 15 and standard deviation  σ \text { σ } = 3.Use the approximate areas beneath the normal curve,as discussed in this section,to find P(9 ≤ x ≤ 21).

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If the z-value for a given value x of the random variable x is z = 1.96,and the distribution of x is normally distributed with a mean of 60 and a standard deviation of 6,then the x-value that this z-value corresponds to is:

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In 1997,private planes had 1.5 fatal crashes per 100 thousand flying hours.Assume a continuous random variable with a exponential distribution.A national association of private plane owners has 560 members who fly 1.5 million miles each year.The mileage crash rate has been estimated to be 20 per 100 million miles of air travel.What is the probability that the next crash by a member of the association will not occur until more than one year from now?

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Like the normal distribution,the exponential density function f(x):

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An efficiency expert makes periodic checks for weighting errors for a long distance shipping firm.The expert inspects for errors in weighing,in recording weights,and errors in processing the bills of lading.Based on past records,the number of weekly errors for all shipments averages 5.30 with a standard deviation of 1.23,and the frequency histogram approximates a normal distribution.Suppose x is the number of weighing errors that will occur next week. Compute the approximate probability for (4 ≤ x ≤ 7).

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The z-score representing the 75th percentile of the standard normal distribution is:

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For a normal curve,if the mean is 20 minutes and the standard deviation is 5 minutes,then the area between 11 and 19 minutes is:

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