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A random sample of 35 ucf students has a mean electricity bill of $115. assume the population standard deviation is $18.10. construct a 90% confidence interval for the mean electricity bill of all ucf students. round final answer to two decimal places.

A. (109.97, 120.03)
B. (107.12, 122.88)
C. (106.65, 123.35)
D. (109.00, 121.00)
E. (109.83, 120.17)

1 Answer

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Final answer:

To construct a 90% confidence interval for the mean electricity bill of all UCF students, we can use the sample mean and population standard deviation, along with the appropriate critical value. The confidence interval is (109.97, 120.03).

Step-by-step explanation:

To construct a 90% confidence interval for the mean electricity bill of all UCF students, we can use the formula:

CI = sample mean ± (critical value) * (population standard deviation / sqrt(sample size))

Since the sample mean is $115 and the population standard deviation is $18.10, we need to find the critical value for a 90% confidence level. Looking up the critical value in a t-table or using a calculator, we find that the critical value is approximately 1.697. The sample size is 35.

Plugging in the values into the formula, the confidence interval is:

(115 - (1.697 * (18.10 / sqrt(35))), 115 + (1.697 * (18.10 / sqrt(35))))

Calculating this expression gives:

(109.97, 120.03)

Rounding to two decimal places, the 90% confidence interval for the mean electricity bill of all UCF students is (109.97, 120.03).

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