Question

The scores of students on an exam are normally distributed with a mean of 250 and a standard deviation of 40. (a) What is the first quartile score for this exam? (Recall that the first quartile is the value in a data set with 25% of the observations being lower.) Answer: (b) What is the third quartile score for this exam? Answer:

Answer 1

Given that,

mean =  = 250

standard deviation =  = 40

Using standard normal table,

P(Z < z) = 25%

=(Z < z) = 0.25  

= P(Z < z ) = 0.25

z =-0.67   

Using z-score formula  

x = z +

x = -0.67*40+250

x = 223.2

b.

third quartile

Using standard normal table,

P(Z < z) = 75%

=(Z < z) = 0.75  

= P(Z < z ) = 0.75

z =0.67   

Using z-score formula  

x = z +

x = 0.67*40+250

x = 276.8