Question

Use the normal distribution of SAT critical reading scores for which the mean is 511 and the standard deviation is 108. Assume the variable x is normally distributed. left parenthesis a right parenthesis What percent of the SAT verbal scores are less than 675​? left parenthesis b right parenthesis If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 550​?

Answer 1

Solution :

Given that ,

mean = = 511

standard deviation = = 108

a ) P(x < 675 ) = P[(x - ) / < (675-511) /108 ]

= P(z < 1.52 )

= 0.9357

Probability = 0.9357

b)

P(x >550 ) = 1 - P(x < 550 )

= 1 - P[(x - ) / < (550- 511) /108 ]

= 1 - P(z < 0.36 )

= 1- 0.6406 = 0.3594

Probability = 0.3594