Question

Let the random variable X follow a normal distribution with µ = 18 and σ = 4. The probability is 0.99 that X is 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 L.

Answer 1

P ( a < X < b ) = 0.99
Dividing the area 0.99 in two parts we get 0.99/2 = 0.495
since 0.5 area in normal curve is above and below the mean
Area below the mean is a = 0.5 - 0.495
Area above the mean is b = 0.5 + 0.495
Looking for the probability 0.005 in standard normal table to calculate critical value Z = -2.58
Looking for the probability 0.995 in standard normal table to calculate critical value Z = 2.58

-2.58 = ( X - 18 ) / 4
a = 7.68
2.58 = ( X - 18 ) / 4
b = 28.32
P ( 7.68 < X < 28.32 ) = 0.99

Smaller value L = 7.68