Bob Nale is the owner of Nale\'s Quick Fill. Bob would like to estimate the mean
ID: 3156894 • Letter: B
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 2.30 gallons. From his records, he selects a random sample of 70 sales and finds the mean number of gallons sold is 6.20. (a) What is the point estimate of the population mean? (Round your answer to 2 decimal places.) Point estimate (b) Determine a 90% confidence interval for the population mean. (Round your answers to 2 decimal places.) Confidence interval and .
Explanation / Answer
a)
It is the sample mean,
Best point estimate = 6.20 [ANSWER]
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b)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 6.2
z(alpha/2) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 2.3
n = sample size = 70
Thus,
Margin of Error E = 0.452174506
Lower bound = 5.747825494
Upper bound = 6.652174506
Thus, the confidence interval is
( 5.747825494 , 6.652174506 ) [ANSWER]