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.

Question

Ashton Carr

Mathematics

13 December, 23:54

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.

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Answers (1)

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Juliet Haney · 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