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 1.80 gallons. From his records, he selects a random sample of 80 sales and finds the mean number of gallons sold is 6.7

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

B. Determine a 95% confidence interval for the population mean. (Use z Distribution Table.) (Round your answers to 2 decimal places.)

Solution

a)

Point estimate = sample mean = 6.7 [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 =    0.025          
X = sample mean =    6.7          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    1.8          
n = sample size =    80          
              
Thus,              
Margin of Error E =    0.394435143          
Lower bound =    6.305564857          
Upper bound =    7.094435143          
              
Thus, the confidence interval is              
              
(   6.305564857   ,   7.094435143   ) [ANSWER]