Suppose that the weight (in ounces) of a major league baseball is a random varia

Question

Suppose that the weight (in ounces) of a major league baseball is a random variable with mean weight mu = 5 and standard deviation sigma = 0.4. A carton contains 100 baseballs. Assume that the weights of the individual baseballs are independent, and let Y represent the total weight of all the baseballs in the carton. (a) Find the expected total weight, mu_y = E(Y). (b) Find the variance, sigma^2 _T. (c) Use the Central Limit Theorem to approximate the probability that the total weight of the baseballs in the carton is a maximum of 503 ounces.

Explanation / Answer

a) mean=5*100=500

b) variance =(0.4)2*100 =16

c)as std deviation =(16)1/2 =4

hence P(X<503)=P(Z<(503-500)/4)=P(Z<0.75)=0.7734

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