Question

Use the normal distribution of SAT critical reading scores for which the moon is 502 and the standard deviation is 122. Assume the variable x is normally distributed

(a) What percent of the SAT verbal scores are less than 650?

(b) 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575?

Answer 1

Solution :

Given that ,

mean = = 502

standard deviation = = 122

a) P(x < 650) = P[(x - ) / < (650 - 502) / 122 ]

= P(z < 1.21)

Using z table,

= 0.8869

b) n = 1000

P(x > 575) = 1 - p( x< 575 )

=1- p P[(x - ) / < (575 - 502) / 122]

=1- P(z < 0.60)

Using z table,

= 1 - 0.7257

= 0.2743

0.2743 * 1000 = 274.3

= 274