Question

Use drawings only ( step 2 through 6), and make sure to shade appropriate areas.

Suppose we are given a normal distribution with u=77, sigma=5 degree fahreheit. we are told that the probability that x is between xo and x1 is po=0.9. what is the value for xo and x1.

Answer 1

Given that,

mean = = 77

standard deviation = = 5

middle

P(-z < Z < z) = 0.9

P(Z < z) - P(Z < -z) = 0.9

2 P(Z < z) - 1 = 0.9

2 P(Z < z) = 1 + 0.9 = 1.9

P(Z < z) = 1.9 / 2 = 0.95

P(Z <1.64 ) = 0.95

z  ± 1.64 using z table

Using z-score formula  

x= z * +

x= -1.64*5+77

x= 68.8

z = 1.64

Using z-score formula  

x= z * +

x= 1.64*5+77

x= 85.2

answer X0=68.8 and X1=85.2