Question

A distribution of values is normal with a mean of 225.5 and a standard deviation of 86.5.

Find P₄₉, which is the score separating the bottom 49% from the top 51%.
P₄₉ =

Answer 1

Solution:-

Given that,

mean = = 225.5

standard deviation = = 86.5

Using standard normal table,

P(Z < z) = 49%

= P(Z < z ) = 0.49

= P(Z < -0.03 ) = 0.49  

z = -0.03

Using z-score formula,

x = z * +

x = -0.03 * 86.5 + 225.5

x = 222.9

P49 = 222.9