Question
In: Statistics and Probability
Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean...
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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 1.90 gallons. From his records, he selects a random sample of 75 sales and finds the mean number of gallons sold is 5.40. |
| a. |
What is the point estimate of the population mean? (Round your answer to 2 decimal places.) |
| Point estimate |
| b. |
Determine a 99% confidence interval for the population mean. (Use z Distribution Table.) (Round your answers to 2 decimal places.) |
| Confidence interval |
Solutions
Expert Solution
Solution :
Given that,
a)
Point estimate = sample mean = 
= 5.40
Population standard deviation = 
= 1.90
Sample size = n = 75
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2
= Z0.005 = 2.576
Margin of error = E = Z/2* ( /
= 2.576 * ( 1.90/
= 0.57
At 99% confidence interval estimate of the population mean is,
- E < 
< + E
5.40 - 0.57 < < 5.40 + 0.57
4.83 < < 5.97
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