Question

. Bob is the owner of Nale’s Texaco Gas Town and he would like to estimate the mean number of litres (L) of gasoline sold to his customers. Assume that the number of litres sold follows the normal distribution with a standard deviation of 8 L. From his records, he selects a random sample of 65 sales and finds the mean number of litres sold is 45. (3 marks) 1) Develop a 80% confidence interval for the population mean. (include the unit) 2) Would it be reasonable to conclude that the population mean is 38L? Why?

Answer 1

Question 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 45

σ = 8

n = 65

Confidence level = 80%

Critical Z value = 1.2816

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 45 ± 1.2816*8/sqrt(65)

Confidence interval = 45 ± 1.2717

Lower limit = 45 - 1.2717 = 43.73

Upper limit = 45 + 1.2717 = 46.27

Confidence interval = (43.73, 46.27)

Question 2

It would not be reasonable to conclude that the population mean is 38L, because the value 38 is not lies between the above interval.