At a very large university, the mean weight of male students is 197.3 pounds with a...

At a very large university, the mean weight of male students is 197.3 pounds with a standard deviation of 15.2 pounds. Let us assume that the weight of any student is independent from the weight of any other student. Suppose, we randomly select 256 male students from the university and look at the weight of each student in pounds. Let M be the random variable representing the mean weight of the selected students in pounds. Let T = the random variable representing the sum of the weights of the selected students in pounds.

a) What theorem will let us treat T and M as normal random variables?

Central Limit Theorem

Monte Carlo Theorem

Chebychev's Theorem

Law of Large Numbers

Convolution Theorem

b) What is the expected value of T?

c) What is the standard deviation of T?

d) If TK is T measured in kilograms (use 1kg = 2.2 pounds), then what is the standard deviation of TK?

e) What is the approximate probability that T is greater than 51,200?

f) What is the standard deviation of M?

g) What is the approximate probability M is between 197 and 198?

h) What is the approximate probability that T is within 2 standard deviations of its expected value?

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Expert Solution

orchestra answered 1 year ago

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