Question

Let the random variable *X* follow a normal distribution
with *µ* = 22 and *σ* = 4. The probability is 0.90
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 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

Let the random variable X follow a normal distribution with µ =
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smaller of the two numbers and U is the larger of the two numbers).
Calculate L.

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A random sample of n = 50 is obtained with a sample mean, X-Bar
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Please explain how to get the answer

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