Question

Assume that all SAT scores are normally distributed with a mean u = 1518 and a standard deviation o = 325. If 100 SAT scores (n = 100) are randomly selected, find the probability that the scores will have an average less than 1500. TIP: Make the appropriate z-score conversion 1st, and then use Table A-2 (Table V) to find the answer. 0.2912 -0.55 0.55 0.7088

Answer 1

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( < 1500) we need to find the Z score which is calculated as:

T

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

T