Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

The director of a customer service center wants to estimate the mean number of customer calls the center handles each day, so he randomly samples 29 different days and records the number of calls each day. The sample yields a mean of 279.4 calls with a standard deviation of 25.1 calls per day. He can be 99% confident that the mean number of calls per day is between 266.5 and ________. (Round your answer to 1 decimal place.)

Sagot :

Answer:

He can be 99% confident that the mean number of calls per day is between 266.5 and 292.3.

Step-by-step explanation:

Confidence interval:

A confidence interval is symmetric, which means that the difference between the sample mean and the lower bound is the same as the difference between the upper bound and the sample mean.

In this question:

Sample mean: 279.4 calls

Lower bound: 266.5 calls

Upper bound: x calls

Due to the symmetry of the confidence interval:

[tex]x - 279.4 = 279.4 - 266.5[/tex]

[tex]x = 12.9 + 279.4[/tex]

[tex]x = 292.3[/tex]

So

He can be 99% confident that the mean number of calls per day is between 266.5 and 292.3.

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.