The University of Montana admission standards require students to have an ACT score of at least 22. We know that Montana ACT scores are normally distributed with a mean of 20.1 and a standard...

The University of Montana admission standards require students to have an ACT score of at least 22. We know that Montana ACT scores are normally distributed with a mean of 20.1 and a standard deviation of 4.

a. Compute the z-score for an ACT score of 22.

b. What is the probability of getting at least a 22 on the ACT? Turn in a normal distribution that is labeled with the mean and standard deviation of the distribution, the value 22, and that is correctly shaded to compute the probability that a student from Montana will have an ACT score of at least 22.

c. If we ask a random sample of 100 students who took the ACT, how many would be expected to qualify for admission to UM?

d. Students in Oregon have a mean ACT score of 21.1 with a standard deviation of 2.8. If we chose one student each at random from Oregon and from Montana, which student would be more likely to meet the ACT requirements of the University of Montana? Explain your answer using the appropriate statistics and a correctly labeled and shaded normal distribution.