The average price of a college math textbook is $160 and the standard deviation is $27. Suppose that 46textbooks are randomly chosen. Round all answers to 4 decimal places where possible.a. What is the distribution of ? - N(b. For the group of 46, find the probability that the average price is between $161 and $165.c. Find the first quartile for the average textbook price for this sample size. $nearest cent)d. For part b), is the assumption that the distribution is normal necessary? O No Yes(round to the

Answered: Image /qna-images/answer/602b8b1a-7b6c-46f4-af80-96e40db43c8f.jpg (b) Obtain the probability that average price is between $161 and $165 for the sample of 46. The probability that average price is between $161 and $165 for the sample of 46 is obtained below as follows: The required probability is, The probability that average price is between $161 and $165 for the sample of 46 is 0.2975.(c ) Obtain the first quartile for the average textbook price for this sample size. The first quartile for the average textbook price for this sample size is obtained below as follows: Consider, Procedure for finding the critical value of z is listed below: Follow the instruction to obtain the critical value of z: Open EXCEL Go to Formula bar. In formula bar enter the function as“=NORMINV” Enter the probability as 0.25. Enter the mean as 0 and the Standard deviation as 1. Click enter EXCEL output: From the EXCEL output, the critical value of z at the probability of 0.25 is –0.6745. The required value of first quartile is, The first quartile for the average textbook price for this sample size is $157.(d) Determine whether the assumption used in part b is necessary to be normal or not. Since, the sample size is large the sampling distribution of mean is approximately normally distributed. Therefore, it is clear that the assumption used in part b is not necessary to be normal because of larger sample size. Correct option: No