SOLUTION: Given a normal distribution with the mean = 100 and standard deviation = 10, if you select a sample of n=25, what is the probability that X is there is a 65% chance that X is above

Question 764122: Given a normal distribution with the mean = 100 and standard deviation = 10, if you select a sample of n=25, what is the probability that X is there is a 65% chance that X is above what value? Need step by step please.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We consult the normal distribution z-table for the z-value that gives a probability of .35 - the corresponding z-value is 1.03.
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The sample mean is the mean of the normal distribution, however, the sample standard deviation is equal to the standard deviation of the normal distribution divided by the square root of n (25). So we have
sample standard deviation = 10 / sqrt(25) = 2
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now we want 1.03 = (x - 100) / 2
x-100 = 2.06
x = 102.06
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we have p(x < 102.06) = .35, so
p(x > 102.06) = 1 - p(x < 102.06) = (1 - .35) = .65
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