The mean lifetime of a tire is 48 months with a standard deviation of 7 months. If 147 tires are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.83 months? Round your answer to four decimal places.

0.9251

Step-by-step explanation:

z = (x-μ)/σ/√n where

x is the raw score

μ is the population mean

σ is the population standard deviation.

n is the random number of samples

(x-μ) = 0.83 months

σ = 7

n = 147

z = 0.83/7/√147

z = 0.83/0.5773502692

z = 1.43760217026

z ≈ 1.44

Determining the probability of the z score from the z table.

P(x<Z) = 0.92507

Approximately to 4 decimal places = 0.9251

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