320_hw6 - each of the following calculate the probabilities...

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Economics 320: Homework 6 Continuous Distributions: Uniform and Normal 1. America West Airlines reports the flight time from Los Angeles to Las Vegas is 65 minutes. Suppose the actual flying time is uniformly distributed between 60 and 70 minutes. a. Show a graph of the continuous probability distribution – draw the probability density function. b. What is the mean flight time? c. What is the variance of the flight times? d. What is the probability that the flight time is less than 68 minutes? e. What is the probability that the flight takes more than 64 minutes? 2. Let the random variable Z follow a standard normal distribution. Find the following. a. P(Z < 1.20) b. P(Z > 1.33) c. P(Z < -1.70) 3.Suppose random variable Y is normally distributed with mean 200 and variance 6400. For
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Unformatted text preview: each of the following calculate the probabilities using the standard normal table. a. P(y&gt;80) b. P(y&lt;20) c. P(120 &lt;y&lt; 305.2) d. P(y&lt;-28.8) e. P(-31.2&lt;y&lt; 23.2) 4.Suppose random variable Y is normally distributed with mean 200 and variance 6400. In each statement find value of A. a. P(y&gt;A)=0.005 b. P(y&lt;A)=0.55 5. Suppose that the following hold true for Y in problem 1. In each statement find values of A and B. Assume that A and B are symmetrical about the mean. a. P(A &lt;y&lt; B)= 0.6826 b. P(A &lt;y&lt; B)= 0.9544 6. Suppose f(z) is the probability density function of standard normal random variable. Evaluate a. -1 . 2 2 . 1 ) ( dz z f Z b. -5 . 5 . ) ( dz z f Z...
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