The weights of four randomly and independently selected bags of potatoes labeled 20.0 pounds were found to be 20.9​, 21.5​, 20.5​, and 21.2 pounds. Assume Normality. Answer parts​ (a) and​ (b) below....

The weights of four randomly and independently selected bags of potatoes labeled 20.0 pounds were found to be 20.9​, 21.5​, 20.5​, and 21.2 pounds. Assume Normality. Answer parts​ (a) and​ (b) below.

a. Find a​ 95% confidence interval for the mean weight of all bags of potatoes.  ​(Type integers or decimals rounded to the nearest hundredth as needed. Use ascending​ order.)

b. b. Does the interval capture 20.0 ​pounds? Is there enough evidence to reject a mean weight of 20.0 ​pounds?

Extracted text: The weights of four randomly and independently selected bags of potatoes labeled 20.0 pounds were found to be 20.9, 21.5, 20.5, and 21.2 pounds. O Assume Normality. Answer parts (a) and (b) below. a. Find a 95% confidence interval for the mean weight of all bags of potatoes. OD (Type integers or decimals rounded to the nearest hundredth as needed. Use ascending order.) b. Does the interval capture 20.0 pounds? Is there enough evidence to reject a mean weight of 20.0 pounds? O A. The interval captures 20.0 pounds, so there is enough evidence to reject a mean weight of 20.0 pounds. It is not plausible the population mean weight is 20.0 pounds. O B. The interval does not capture 20.0 pounds, so there is enough evidence to reject a mean weight of 20.0 pounds. It is not plausible the population mean weight is 20.0 pounds. O c. The interval captures 20.0 pounds, so there is not enough evidence to reject a mean weight of 20.0 pounds. It is plausible the population mean weight is 20.0 pounds. O D. The interval does not capture 20.0 pounds, so there not is enough evidence to reject a mean weight of 20.0 pounds. It is plausible the population mean weight is 20.0 pounds. O E. There is insufficient information to make a decision regarding the rejection of 20.0 pounds. The sample size of 4 bags is less than the required 25.