Bob Nale is the owner of Nale\'s Quick Fill. Bob would like to estimate the mean

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 2.50 gallons. From his records, he selects a random sample of 55 sales and finds the mean number of gallons sold is 5.40. What is the point estimate of the population mean? (Round your answer to 2 decimal places.) Point estimate Determine a 90 percentage confidence interval for the population mean. (Round your answers to 2 decimal places.) Confidence interval

Explanation / Answer

a.
Point of estimate =Mean(x)=5.4
b.
Confidence Interval
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

Standard deviation( sd )=2.5
Sample Size(n)=55
Confidence Interval = [ 5.4 ± Z a/2 ( 2.5/ Sqrt ( 55) ) ]
= [ 5.4 - 1.64 * (0.34) , 5.4 + 1.64 * (0.34) ]
= [ 4.85,5.95 ]

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