Question

2. In a given year the Murphy College admissions office accepts applications from students, who are then either accepted or not-accepted. Accepted students may or may not decide to attend Murphy College. Suppose the scores on a certain entrance exam for applicants of Murphy College follow the normal distribution with mean 1600 and standard deviation 300.

a. What is the probability that a given applicant has a score of more than 2050?
b. What is the probability that a given applicant has a score of between 1450 and 1900?
c. Suppose that top scoring applicants are award merit scholarship money based on their scores. Suppose that any student scoring above 1900 is awarded $20,000 in scholarship money. If 1000 students apply to Murphy College in a given year, how much money does the college award in total?
d. How would Murphy College calculate the expected amount (in $) of merit scholarships dispersed in a given year?

Answer 1

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.