Question

Suppose x is a normally distributed random variable with muμequals=32 and sigmaσequals=4

Find a value x 0x0 of the random variable x.

a. ​P(xgreater than or equals≥x 0x0​)equals=.5

b. ​P(xless than<x 0x0​)equals=.025

c. ​P(xgreater than>x 0x0​)equals=.10

d. ​P(xgreater than>x 0x0​)equals=.95

Answer 1

Part a)

P ( X >= ? ) = 1 - P ( X < ? ) = 1 - 0.5 = 0.5
Looking for the probability 0.5 in standard normal table to calculate critical value Z = 0

0 = ( X - 32 ) / 4
X = 32
P ( X >= 32 ) = 0.5

Part b)

P ( X < ? ) = 2.5% = 0.025
Looking for the probability 0.025 in standard normal table to calculate critical value Z = -1.96

-1.96 = ( X - 32 ) / 4
X = 24.16
P ( X < 24.16 ) = 0.025

Part c)

P ( X > ? ) = 1 - P ( X < ? ) = 1 - 0.1 = 0.9
Looking for the probability 0.9 in standard normal table to calculate critical value Z = 1.28

1.28 = ( X - 32 ) / 4
X = 37.12
P ( X > 37.12 ) = 0.1

Part d)

P ( X > ? ) = 1 - P ( X < ? ) = 1 - 0.95 = 0.05
Looking for the probability 0.05 in standard normal table to calculate critical value Z = -1.64

-1.64 = ( X - 32 ) / 4
X = 25.44
P ( X > 25.44 ) = 0.95