Complete the following:
1. a) A random sample of 100 managers in Alaska had an average yearly income of $125,500 with a standard deviation of $20,000. Develop the 95%, 90%, and 99% confidence intervals for the yearly income of all managers in Alaska.
b) If we assume we know the standard deviation of yearly income of all managers in Alaska is $25,000, build the 95%, 90%, and 99% confidence intervals for the average yearly income of all managers in Alaska.
2. The IQ scores of a population of students have mean 100 and standard deviation 15. If a sample of 100 students is selected, find the probability that sample mean of their IQ scores will lie between 95 and 130. If the sample size increases to 200 students, what is the corresponding probability?
3. A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation, the proper distribution to use should be a t distribution with 199 degrees of freedom (True or False)