# statistics

at a bank, account balances are nomrally distribued with a mean of \$637.52 and standard deviation of \$623.16. What is the probability that a simple randon same of 400 accounts has mean that exceeds \$1650.00? show me steps and calculations i urgently need help

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1. I think you either have a typo or the problem wanted to be out of reasonable range. Are you sure not \$650, not \$1650 ???
Anyway here is a method:
Sample Mean also has normal distribution
The mean will have the same mean as the original.
However the sigma = original sigma /sqrt(sample size) = 623.16/20
= 31.15
So
The real question is in a normal distribution with mean = 637.52 and sigma = 31.15 what is the probability of over 1650?
how far above mean? (1650 - 637.52) = 1012.48
how many sigmas above mean?
1012.48 / 31.15 = 32.5 sigmas from mean
That is off any table of normal distribution. It is so improbable that the online normal distribution calculators just return zero.
So, lets see what the probability is of the opposite, the mean lying between 0 and 32.5 sigma. It is of course .5
In other words the probability of the sample being beyond 32.5 sigma is so tiny the calculators will not do it.

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posted by Damon
2. NOW
What if you had said \$650 ?????

The real question is in a normal distribution with mean = 637.52 and sigma = 31.15 what is the probability of over 650?
how far above mean? (650 - 637.52) = 12.48
how many sigmas above mean?
12.48 / 31.15 = .401 sigmas from mean
So from table, what is probability beyond .401 sigma above mean ?
from normal distribution table F(.400) = .345

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posted by Damon

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