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Assume that all SAT scores are normally distributed with a mean u = 1518 and a standard deviation o = 325. If 100 SAT scores

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Given the scores are normally distributed with mean \mu = 1518 and the standard deviation as \sigma = 325, now if a sample of n = 100 is selcted then to calculate the probability that the mean score of sample is less than 1500 P( T < 1500) we need to find the Z score which is calculated as:

X - μ Z 1500 – 1518 325/ 100 -0.5538 own

Z = -0.55

Now the probability is calculated using the excel formula for normla distribution which is =NORM.S.DIST(-0.55, TRUE), thus the probability is computed as:

P( T < 1500) = P( Z< 0.55) = 0.2912.

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