Question

It has been found that scores on the Writing portion of the SAT (Scholastic Aptitude Test) exam are normally distributed with mean 484 and standard deviation 115. Use the normal distribution to answer the following questions.

(a) What is the estimated percentile for a student who scores 475 on Writing?

(b) What is the approximate score for a student who is at the 90th percentile for Writing?

Answer 1

Solution :

Given that,

mean = = 484

standard deviation = = 115

P(X< 475) = P[(X- ) / < (475-484) /115 ]

= P(z <-0.08 )

Using z table

= 0.4681

=46.81%

b.

Using standard normal table,

P(Z < z) = 90%

= P(Z < z) = 0.90  

z = 1.28 Using standard normal z table,

Using z-score formula  

x= z * +

x= 1.28*115+484

x= 631.2