Question

For normally distributed data with μ = 100, and σ = 10, what value of x in the right tail has 0.40 area between the mean and x?

Answer 1

P(X < A) = P(Z < (A - )/)

= 100

= 10

Area between mean and x in the right tail = 0.40

That is P(100 < X < x) = 0.40

P(X < x) = 0.5 + 0.4 = 0.90

P(Z < (x - 100)/10) = 0.90

Take the value of z corresponding to 0.90 from standard normal distribution table.

(x - 100)/10 = 1.28

x = 1.28 x 10 + 100

x = 112.8