Question

Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of 2.40 gallons. From his records, he selects a random sample of 45 sales and finds the mean number of gallons sold is 6.80.

1. What is the point estimate of the population mean? (Round your answer to 2 decimal places.)

2. Develop a 90% confidence interval for the population mean. (Use zDistribution Table.) (Round your answers to 2 decimal places.)

Confidence Interval____ and _____

Answer 1

Part a)

Point estimate = X̅ = 6.80

Confidence Interval :-
X̅ ± Z( α /2) σ / √ ( n )
Z(α/2) = Z (0.1 /2) = 1.645
6.8 ± Z (0.1/2 ) * 2.4/√(45)
Lower Limit = 6.8 - Z(0.1/2) 2.4/√(45)
Lower Limit = 6.21
Upper Limit = 6.8 + Z(0.1/2) 2.4/√(45)
Upper Limit = 7.39
90% Confidence interval is ( 6.21 , 7.39 )