A random variable is known to be normally distributed with the parameters shown

Question

A random variable is known to be normally distributed with the parameters shown below. Complete parts a and b. = 6.8 and 0.60 a. Determine the value of x such that the probability of a value from this distribution exceeding x is at most 0.40. (Round to three decimal places as needed.) b. Referring to your answer in part a, what must the population mean be changed to if the probability of exceeding the value of x found in part a is reduced from 0.40 to 0.20? (Round to three decimal places as needed.)

Explanation / Answer

Ans:

Given that

mean=6.8,standard deviation=0.6

a)

P(X>=x)=0.4

P(Z<=z)=0.4

P(Z<z)=1-0.4=0.6

z=0.2533

x=6.8+0.2533*0.6=6.952

b)

P(Z>=z)=0.2

P(Z<=z)=0.8

z=0.8416

0.8416=(6.952-mean)/0.6

mean=6.952-0.8416*0.6=6.447

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