Question

Save & End Certify Lesson: 9.3 The Distribution of the Sample... ANNIE PORTER - Question 5 of 13, Step 1 of 1 3/13 Correct The mean life of a television set is 121 months with a variance of 256. If a sample of 95 televisions is randomly selected, what is the probability that the sample mean would be less than 118.8 months? Round your answer to four decimal places Tables Keypad Answer How to enter your answer

Answer 1

Using Central limit theorem, the distribution for the sample mean is given as:

Χο Νίμ = μΧ, σ =

V256 X Nu=121,0 =- 95

X Nu= 121,0 = 1.6416)

The probability now is computed as:

P(X < 118.8)

Converting it to a standard normal variable, we get here:

P(Z <- 118.8 - 121 1.6416

P(Z < -1.3402)

Getting it from the standard normal tables, we get here:

P(z<-1,3402) = 0,0901

Therefore 0.0901 is the required probability here.