Suppose the average number of returns processed by employees of a tax preparation service during tax season is 11 per day with a standard deviation of 4 per day. A random sample of 36 employees taken during tax season revealed thenumber of returns processed daily shown below. Use these data to answer parts a through c.16171311101316161315141411131611 D109 716151181314119.186.42381120a. What is the probability of having a sample mean equal to or smaller than the sample mean for this sample if the population mean is 11 processed returns daily with a standard deviation of 4 returns per day?The probability is:(Round to four decimal places as needed.)b. What is the probability of having a sample mean larger than the sample mean for this sample if the population mean is 11 processed returns daily with a standard deviation of 4 returns per day?The probability is.(Round to four decimal places as needed.)c. Explain how it is possible to answer parts a and b when the population distribution of daily tax returns at the tax firm is not known. Choose the correct answer below.A. The Central Limit Theorem can be applied because the sample size is sufficiently large. Thus, the distribution of the sample means will be either skewed to the left or skewed to the right.O B. All data are normally distributed. Thus, the distribution of the sample means will be approximately normal.C. The Central Limit Theorem can be applied because the sample size is sufficiently large. Thus, the distribution of the sample means will be approximately normal.O D. The Central Limit Theorem can be applied because the sample size is not large. Thus, the distribution of the sample means will be approximately normal.Click to select your answer(s).MacBook Proesc20888%23$&234578EYUPT

Solution: Given information: n= 36 Sample size μ=11 Population mean σ=4 Population standard…

Suppose the average number of returns processed by employees of a tax preparation service during tax season is 11 per day with a standard deviation of 4 per day. A random sample of 36 employees taken during number of returns processed daily shown below. Use these data to answer parts a through c. 16 17 13 11 10 13 16 16 13 15 14 14 11 13 10 16 15 11 13 14 11 18 23 8 a. What is the probability of having a sample mean equal to or smaller than the sample mean for this sample if the population mean is 11 processed returns daily with a standard deviation of 4 returns per day? The probability is (Round o four decimal places as needed.) b. What is the probability of having a sample mean larger than the sample mean for this sample if the population mean is 11 processed returns daily with a standard deviation of 4 returns per day? The probability is O (Round to four decimal places as needed.) c. Explain how it is possible to answer parts a and b when the population distribution of daily tax returns at the tax firm is not known. Choose the correct answer below. O A. The Central Limit Theorem can be applied because the sample size is sufficiently large. Thus, the distribution of the sample means will be either skewed to the left or skewed t o the right. O B. All data are normally distributed. Thus, the distribution of the sample means will be approximately normal. OC. The Central Limit Theorem can be applied because the sample size is sufficiently large. Thus, the distribution of the sample means will be approximately normal. OD. The Central Limit Theorem can be applied because the sample size is not large. Thus, the distribution of the sample means will be approximately normal.

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA