Bob Nale is the owner of Nales Quick Fill Bob would like to

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 2.30 gallons. From his records, he selects a random sample of 60 sales and find the mean number of gallons sold is 8.60.

A. What is the point estimate of the population mean?

B. Develop a 99% confidence interval for the population mean.

C. Interpret the meaning of part b

Solution

a)
Point of estimate (x)=8.6
b)
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=8.6
Standard deviation( sd )=2.3
Sample Size(n)=60
Confidence Interval = [ 8.6 ± Z a/2 ( 2.3/ Sqrt ( 60) ) ]
= [ 8.6 - 2.58 * (0.297) , 8.6 + 2.58 * (0.297) ]
= [ 7.834,9.366 ]
c)
we are 99% confident the population mean always lies in the in the ineterval
stated in b