Question

1. In 2019, the average SAT score for an admitted student to VCU was 1180 with a standard deviation of 160. If these times were normally distributed, what is the probability a student chosen at random will have a SAT score of less than 1050? Would this be unusual?

Answer 1

= 1180,  = 160, x=1050

We want to find P( x < 1050)

formula is

z =  −0.8125

z = -0.81

P( x < 1050) = P (z < -0.81)

find  P (z < -0.81) using normal z table e get,

P (z < -0.81) = 0.2083

P( x < 1050) =  0.2083

Probability a student chosen at random will have a SAT score of less than 1050 = 0.2083

Z score outside ( -2 and 2 ) are considered as unusual.

here Z score calculated is ls z =-0.81

Hence, 1050 is not unusual.