The distribution of sample sums

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Question from Mark, a student:

I have another problem i can't solve. Could you help me?

here is the question.

For large samples, the sample sum (Σ x) has an approximately normal distribution.
The mean of the sample sum is n*μ and standard deviation is (σ*√n). The distribution of savings per account for savings and loan institution has a mean equal to $750 and a standard deviation equal to $25. For a sample of 50 such accounts, find the probability that the sum in the 50 accounts exceeds $38,000.

thanks alot for your help in advance.

Mark,

This is very similar to the problem you mention. You have a normal distribution so you need to convert it to the standard normal distribution, set up the probability statement as a mathematical expression and use the standard normal table to determine the probability. In the current problem the mean of the distribution is n × μ = 50 × $750 = $37, 500 and the standard deviation is σ × √n = $25 × √50.

Harley

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