A distribution of values is normal with a mean of 176.6 and a standard deviation of 23.5. Find P61, which is the score separating the bottom 61% from the top 39%. P61 =

Question

A distribution of values is normal with a mean of 176.6 and a standard deviation of 23.5.

Find P₆₁, which is the score separating the bottom 61% from the top 39%.

P₆₁ =

Answer 1

P₆₁ = 183.2

(x- 176.6)/23.5 = z score = 0.279 from z tables or a z calculator, corresponding to 39%

x -176.6 = 23.5(.279)

x = 176.6 + 6.56

x= 183.2 = the cutoff between bottom 61% and 39% top scores