Question

Let the random variable X follow a normal distribution with µ = 22 and σ = 4. The probability is 0.90 that Xis in the symmetric interval about the mean between two numbers, L and U (L is the smaller of the two numbers and U is the larger of the two numbers). Calculate U.

Answer 1

P ( a < X < b ) = 0.9
Dividing the area 0.9 in two parts we get 0.9/2 = 0.45
since 0.5 area in normal curve is above and below the mean
Area below the mean is a = 0.5 - 0.45
Area above the mean is b = 0.5 + 0.45
Looking for the probability 0.05 in standard normal table to calculate critical value Z = -1.64
Looking for the probability 0.95 in standard normal table to calculate critical value Z = 1.64

-1.64 = ( X - 22 ) / 4
a = 15.44

1.64 = ( X - 22 ) / 4
b = 28.56

P ( 15.44 < X < 28.56 ) = 0.9

U = 28.56