Question

SAT math score have a bell-shaped distribution with a mean of 515 and standard deviation of 114.

A) what percentage of SAT score is between 401 and 629?
B) what percentage of SAT score is less than 401 or greater than 629?
C) what percentage of SAT score is greater than 743?

Answer 1

Explanation:

Given that SAT math score have a bell-shaped distribution with a mean of 515 and standard deviation of 114.

Since given that bell distribution we can assume that Sat math score is normal with N(515,114)

a)
`P(401<x<629)=P(}z}<(114)/(114) )\\=0.68`

i.e. 68% of SAT score is between 401 and 629

so 32% is either less than401 or >629

b) 743 is 2 std deviations from 515

Hence probability = 0.5-0.4772 =0.0228

i.e. 2.28%