Question 1: The average teacher's salary in Arizona is $42,300 with standard deviation $5000. Assuming a normal distribution, what is the probability that the mean of a sample of 50 teachers' salaries will be at least $48,000 a year?
Question 2: If a baseball player's batting average is 0.275, find the probability that the player will get at least 40 hits in 100 times at bat.
Question 3: Thirty randomly selected vehicles were stopped, and the tread depth of the right front tire was measured. The mean was 0.20 inch, and the standard deviation was 0.05 inch. Find the 95% confidence interval of the mean depth. Assume the variable is approximately normally distributed.
Question 4: A statistics instructor is asked to estimate the average age of students at the college at 99% confidence with accuracy within 2 years. A previous study determined that the standard deviation was 5 years. How large a sample is needed?