Question

Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. find the probability that 70 randomly selected washing machines will have a mean replacement time less than 9.1 years. write your answer as a decimal rounded to 4 places.

Answer 1

The probability will be found as follows:
z-score is given by:
z=(x-μ)/σ
where:
mean-μ=9.3
standard deviation-σ=1.1 
but
σ/√n=1.1/√70=0.1315
thus the z-score will be:
z=(9.1-9.3)/0.1315
z=-1.5209
thus:
P(x<9.1)=P(z<-1.5209)=0.0643