Exam 8: Continuous Probability Distributions

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If the value of Z is z = 99, that means you are at the 99th percentile on the Z distribution.

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Which of the following is true for an exponential distribution with parameter λ\lambda ?

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Suppose Lamont's exam score was at the 80th percentile on an exam whose mean was 90.What was Lamont's exam score?

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The mean and the variance of an exponential distribution are equal to each other.

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Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. -{Waiting Time Narrative} What is the probability that a patient would have to wait no more than one hour?

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The probability density function of a uniform random variable on the interval [0, 5] must be ____________________ for 0 ≤\le x ≤\le 5.

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The shape of the density function for an exponential distribution is ____________________.

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The number of parameters for an F distribution is:

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The y-intercept of the density function for an exponential distribution with parameter 10 is ____________________.

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Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. -{Subway Waiting Time Narrative} What is the probability that the subway arrives in the first minute and a half?

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P(Z > 3.00) is approximately ____________________.

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Use the c2 table to find the following probabilities. a. b. c. d.

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The value of A such that P(-A ≤\le t ≤\le A) = 0.95, where the degrees of freedom are 20, is 2.086.

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Calculus Scores Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4.(Total possible points = 100.) -{Calculus Scores Narrative} What is the probability that a randomly selected student will have a score between 80 and 90?

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The value of an F distribution with v1 = 5 and v2 = 10 degrees of freedom such that the area to its left is 0.95 is 3.33.

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For values of degrees of freedom greater than 100, the c2 distribution can be approximated by a(n) ____________________ distribution.

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If the random variable X is exponentially distributed with parameter λ\lambda = 2, then the probability that X is between 1 and 2 equals the probability that X is between 2 and 3.

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Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes. -{Repair Time Narrative} What is the probability that it will take a technician between 10 to 15 minutes to fix a telephone problem?

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A larger standard deviation of a normal distribution indicates that the distribution becomes:

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P(1 < Z < 2) = P(Z < 2)-____________________.

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