The composite ACT scores of entering freshmen at an area University have a N(24,4) distribution. Use this information to complete the following.
a) For one randomly selected entering freshman, what is the probability that their composite ACT score was greater than 30? (4 points)
b) A random sample of 100 entering freshmen is selected. What is the distribution of the mean composite ACT score, ?, for the University? (4 points)
c. What is the probability that the mean composite ACT score for the 100 randomly chosen freshmen is less than 23? (6 points)
Problem 5. The Hemingway Financial Company prepares tax returns for individuals. According to the Internal Revenue Service, individuals making $50,000 - $ 75,000 are audited at a rate of 3%. The Hemingway Company prepares six tax returns for individuals in that tax bracket, and three of them are audited.
Find the probability that when 6 people making $50,000 - $75,000 are randomly selected, exactly 3 of them are audited?
What is the expected number of audits for the 6 randomly selected individuals?
What is the standard deviation for the number of audits for the 6 randomly selected individuals?