20 points ! 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

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

Ais the correct answer