The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon. Construct a 97.5% confidence interval for the mean gas mileage for this car model.

Answer: confidence interval = 27.5 + / - 1.68

= (25.82, 29.18)

Step-by-step explanation:

Given;

Number of samples n = 64

Standard deviation r = 6mi/gallon

Mean x = 27.5mi/gallon

Confidence interval of 97.5%

Z' = t (0.0125) = 2.24

Confidence interval = x + / - Z' (r/√n)

= 27.5 + / - 2.24 (6/√64)

= 27.5 + / - 1.68

= (25.82, 29.18)