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Complete Question
The mean lifetime of a tire is 42 months with a variance of 49. If 145 tires are sampled, what is the probability that the mean of the sample would be greater than 42.8 months.
Answer:
0.083793
Explanation:
We would be using the z score formula.
z score formula = z = (x - μ)/σ/√n
where
x is the raw score = 42.8
μ is the population mean = 42
σ is the population standard deviation =
In the above question, we were given variance = 49
Standard deviation = √Variance
= √49
= 7
n = number of samples = 145
z score = z = (x - μ)/σ/√n
= (42.8 - 42)/ (7/√145)
= 0.8/ 0.581318359
= 1.37618
Approximately to 2 decimal places= 1.38
Using the z score table to find the probability.
P(x ≤ 42.8) = P(z = 1.38) = 0.91621
P(x>42.8) = 1 - P(x<42.8)
1 - 0.91621
= 0.083793
Therefore, the probability that the mean of the sample would be greater than 42.8 is 0.083793