A company wants to estimate the average time employees spend on a training module. 15 employees are randomly selected, & their completion times recorded. The sample of times to complete the module is normally distributed with mean 42.7 min & std. dev. 5.4 min.
(A) Make a 95% conf. int. for the true mean time to complete the training.

Find the critical val. ($t_{\alpha \text{⁄}2}$) for each confidence interval.

(B) Confidence Level = $90\%,n=48$

Find each probability.

(A) $P(T>1.5),df=8$

Find each probability.

(B)

A nutritionist wants to estimate the average grams of protein in a brand of protein bars. She takes a random sample of 40 protein bars with $\bar{x}=210$ g & knows from prior data that $\sigma =12$. Make a 95% conf. int. for $\mu$.

A company wants to estimate the average time employees spend on a training module. 15 employees are randomly selected, & their completion times recorded. The sample of times to complete the module is normally distributed with mean 42.7 min & std. dev. 5.4 min.

(B) Should management be concerned that the training might take too long if their policy states the module should take at most 45 min? Justify your answer using your confidence interval.

A beverage company claims that on average, customers consume 500 mL of their new energy drink in a single sitting. To test this claim, a market researcher collects a random sample of 8 customers. Assume the sample is normal & make a 90% conf. int. for the true mean volume. Does the data support the company’s claim?

A retailer wants to estimate the average amount spent by customers on holiday shopping. In a random sample of 50 customers, the average amount spent was $250, and the population standard deviation $\sigma$ is known to be $40. Construct and interpret an 80% confidence interval for the average amount spent by all customers.

Books get more and more expensive every semester, but the distribution of their prices is always normal. 25 randomly selected students in your school spent, on average $500 with a standard deviation of $50. Construct a 98% confidence interval for the true spending on books.