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

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