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Unformatted text preview: variable alone, 0.21. 2. Suppose you have a normally distributed random variable, X , with mean μ = 5 and standard deviation σ = 3. You want to know the probability that X < 2. (a) Compute the standardized value of X necessary to look up the probability on the standard normal table. (2 points) Standardize X by subtracting the mean and dividing by the standard deviation: X-μ σ = 2-5 3 =-1 (b) On a standard normal table, you ﬁnd that P ( Z < 1) is approximately 0.84. What is the probability that X < 2? (3 points) Since P ( Z < 1) = 0 . 84, then P ( Z > 1) = 1-. 84 = 0 . 16. Since the normal distribution is symmetric, P ( Z > 1) = P ( Z <-1), so the probability that X < 2 = 0 . 16....
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This note was uploaded on 01/13/2012 for the course ARE 32482 taught by Professor Havenner during the Spring '10 term at UC Davis.
- Spring '10