Question 9 of 14, Step 1 of 1
$8 / 14$
Correct
4
The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. Assume that the population standard deviation is $2 \mathrm{kWh}$. The mean electricity usage per family was found to be $20 \mathrm{kWh}$ per day for a sample of 576 families. Construct the $85 \%$ confidence interval for the mean usage of electricity. Round your answers to one decimal place.
Answer
Tables
Keypad

Step 1 ：The problem is asking for the 85% confidence interval for the mean usage of electricity. The confidence interval can be calculated using the formula: \(\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}\) where \(\bar{x}\) is the sample mean, \(Z\) is the Z-score, which corresponds to the desired confidence level, \(\sigma\) is the population standard deviation, and \(n\) is the sample size.

Step 2 ：In this case, \(\bar{x} = 20\) kWh, \(\sigma = 2\) kWh, and \(n = 576\). The Z-score for an 85% confidence interval is approximately 1.44 (this value can be found in a standard Z-table).

Step 3 ：Let's plug these values into the formula and calculate the confidence interval.

Step 4 ：After running this code, we will observe the lower and upper bounds of the confidence interval. The lower bound is 19.9 and the upper bound is 20.1.

Step 5 ：Final Answer: The 85% confidence interval for the mean usage of electricity is \(\boxed{(19.9, 20.1)}\) kWh per day.