quiz5 with soln

# quiz5 with soln - QUIZ 5 AMS310.01 Monday Print your name...

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QUIZ 5 AMS310.01 Monday, October 20, 2003 Print your name here________________________________________________ ____1. Suppose that X has mean μ =10 and σ =50 and Y= (X-10)/50. The mean of Y equals_____ ____2. Suppose that X is a binomial variable with n=81 and p=0.5. Then μ =np= 40.5 and σ = = - ) 1 ( p np 5 . 0 5 . 0 81 x x = 4.5. Then Pr(X 49) 2245 P(Z ____) = Φ (z) . Find z. 3-4. Suppose X is a continuous random variable with normal histogram. Suppose also that the mean value of X equals 5 and the standard deviation of X equals 3, i.e., μ =5 and σ =3 ____3. Pr{ X < 0}= _______. Hint: Find z. Pr(X<0)= Φ (z). ____4. Find the 95 th percentile for X, i.e. Find c such that P(X<c) = 0.95. Hint : Φ (1.96) = 0.95. Extra Credit: When are Dr. Mendell's office hours? Do you have a class conflicting with both of Dr. Mendell's office hours? Yes____ No_____.

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Solutions to Quiz 5 __0.0__ 1. Suppose that X has mean μ =10 σ =50 and Y= (X-10)/50. The mean of Y equals_____ The mean of Y= 0.0. Y= (X- μ )/ σ = Z score. Mean of Z score = 0.0 and Standard deviation of Z score = 1.0 always. __2.0 (1/2 credit for 1.89 or 17/9) __ 2. Suppose that X is a binomial variable with n=81 and p=0.5. Then μ =np=40.5 and σ = = - ) 1 ( p np 5 . 0 5 . 0 81 x x = 4.5. Then Pr(X 49) 2245 P(Z
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