THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of beverage cans produced each hour from a vending machine is normally distributed with a standard deviation of 8.6.For a random sample of 12 hours,the average number of beverage cans produced was 326.0.Assume a 99% confidence interval for the population mean number of beverage cans produced per hour.
-Calculate the margin of error of the 99% confidence interval.
A)1.85
B)3.60
C)6.41
D)10.56

Question

Quizplus · Accepted Answer

To calculate the margin of error for a 99% confidence interval, we need to use the formula:
Margin of error = Z* (standard deviation / √n)
where Z* is the Z-value corresponding to a 99% confidence level, and n is the sample size.

For a 99% confidence level, the Z-value is 2.576 (obtained from a standard normal distribution table or calculator). Plugging in the values given in the problem, we get:
Margin of error = 2.576 * (8.6 / √12) = 6.41

Therefore, the margin of error for the 99% confidence interval is 6.41, which is option C.