Question

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is21,009 miles with a variance of 6,220,036. What is the probability that the sample mean would differ from the population mean by less than 655 miles in a sample of 79 tires if the manager is correct

Answer 1

The probability that the sample mean would differ from the population mean by less than 655 miles in a sample of 79 tires if the manager is correct is = 0.9805.

What is the calculation for the above?

P ($\bar{x}$ < 655) ≡ P [ |( $\bar{x}$ - μ)/√(σ²/n) | <655/√(6,220,036/ 79)]

= P (| Z | < 3.55)

= P - 3.55 < Z < 3.55) Using the z -score table

= 0.9998 - 0.0193

= 0.9805

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