Find each probability.
(B)

Fill out the table using a calculator and $n=30$.

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

(A) Confidence Level = $95\%,n=35$

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

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

Find each probability.

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

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.

(A) Make a 95% conf. int. for the true mean time to complete the training.

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?