# 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

Algebra ->  Probability-and-statistics -> 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      Log On

 Ad: Mathway solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 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(643)   (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. ============================================================================== 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 ============================================================================== now we want 1.03 = (x - 100) / 2 x-100 = 2.06 x = 102.06 ============================================================================= we have p(x < 102.06) = .35, so p(x > 102.06) = 1 - p(x < 102.06) = (1 - .35) = .65 ==============================================================================