1.
Random-number generators have many uses in statistics. One type is designed
to produce a sequence of numbers between 0 and 1. A number x can assume any
value in the interval from 0 to 1 with equal probability, and any value of x
is independent of values of previous numbers that appear in the sequence.
Furthermore, the probability distribution of x has a mean μ=.5 and a standard
deviation σ=.29. Let y be the average of n such random numbers. Suppose n=40.
Find the approximate probability that the sample mean exceeds .4.
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