Use the normal distribution of SAT critical reading scores f

Use the normal distribution of SAT critical reading scores for which the mean is 503 and the standard deviation is 106 . Assume the variable x is normally distributed. left parenthesis a right parenthesis What percent of the SAT verbal scores are less than 625 ? left parenthesis b right parenthesis If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575 ?

Solution

mean = 503 sd = 106

Z = (X-503)/103

a)P(X<625)

= P(Z<(625-503)/103)

= P(Z< 1.18446)

= 0.8810

hence percentage =

b) P(X >575)

= P(Z> (575-503)/103)

= P(Z>0.6990)

=1-0.7580 = 0.242

hence out of 1000 score , 242 scores are expected to greater than 575.