Answer:
The probability is 0.0643
Step-by-step explanation:
* Lets revise some definition to solve the problem
- The standard deviation of the distribution of sample means is called σM
- σM = σ/√n , where σ is the standard deviation and n is the sample size
- z-score = (M - μ)/σM, where M is the mean of the sample , μ is the mean
of the population
* Lets solve the problem
- The mean of the washing machine is 9.3 years
∴ μ = 9.3
- The standard deviation is 1.1 years
∴ σ = 1.1
- There are 70 washing machines randomly selected
∴ n = 70
- The mean replacement time less than 9.1 years
∴ M = 9.1
- Lets calculate z-score
∵ σM = σ/√n
∴ σM = 1.1/√70 = 0.1315
∵ z-score = (M - μ)/σM
∴ z-score = (9.1 - 9.3)/0.1315 = - 1.5209
- Use the normal distribution table of z to find P(z < -1.5209)
∴ P(z < -1.5209) = 0.06426
∵ P(M < 9.1) = P(z < -1.5209)
∴ P(M < 9.1) = 0.0643
* The probability is 0.0643
.