Question

20 POINTS PLEASE HELP! A normally distributed set of data has a mean of 440 and a standard deviation of 26. Which values separate the bottom 40% and the top 25% of the data?

A.
422.6 and 440.1

B.
450.4 and 459.5

C.
433.5 and 457.4

D.
446.5 and 457.4

Answer 1

The mean of the data set is 440 and the standard deviation is 26. The value separating:
Bottom 40% will be found as follows:
P(X<x)=0.4
P(Z<x)=-0.25
thus
(x-440)/26=-0.25
x-440=-6.5
x=433.5

Top 25% of the data:
P(X>x)=1-P(X<x)=1-0.25=0.75
P(Z<0.75)=0.67
thus
(x-440)/26=0.67
x-440=17.42
x=457.42
The answer is:
C] 433.5 and 457.4