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 $\mu$.

Find the critical val. $\left(t_{\alpha /2}\right)$ for each confidence interval.

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

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

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

Find each probability.

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

Find each probability.

(B)

To study the concentration of a particular pollutant (in parts per million) in a local river, an environmental scientist collects 32 water samples from random locations. They get $\bar{x}=3.87$ ppm & know from previous data that $\sigma =0.62$ ppm. Make a 99% conf. int. for the mean pollutant concentration.

A technician wants to estimate the average battery life of a new type of smart phone, so he tests 8 randomly selected phones & records the data below. Assuming battery life has a normal dist, make a 90% conf. int. for the mean battery life.

Gas prices are getting more and more expensive. The average gas price, from a random sample of 100 gas stations, was $3.50. It is assumed that gas prices have a standard deviation of $0.04. Construct an 80% confidence interval for the true mean gas price in the United States.

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.