Use the normal distribution of SAT critical reading scores for which the mean is

Question

Use the normal distribution of SAT critical reading scores for which the mean is 500 and the standard deviation is 107 Assume the variable x is normally distributed (a) What percent of the SAT verbal scores are less than 625? (b) If 1000 SAT verbal scores are randomly selected. about how many would you expect to be greater than 525? (a) Approximately % of the SAT verbal scores are loss than 625 (Round to two decimal places as needed) (b) You would expect that approximately SAT verbal scores would be greater than 525 (Round to the neatest whole number as needed)

Explanation / Answer

mean = 500
std. dev. = 107

(a)
P(X<625) = P(z < (625-500)/107) = P(z< 1.1682) = 0.8786

Hence 87.86% of the SAT verbal scores are less than 25.

(b)
P(X>525) = P(z> (525 - 500)/107) = P(z > 0.2336) = 0.4076

Out of 1000, 1000*0.4076 = 408 (approximately) SAT verbal scores would be greater than 525.

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