Question 5

An online SAT Test Prep company offers 2 packages to use their services: The Standard package that they claim

will improve a student's SAT score by an average of 40 points and a Premium package that they claim will improve

a student's score by 75 points on average. Thirty students will test out the standard package and 15 students will

test out the more expensive premium package. Assuming a normal distribution with a variance of 1600 for the grade

improvement of each package determine the following.

1. The probability that the average SAT improvement of the students using the premium package will be less than

the average SAT improvement of students using the standard package

2. The probability that the average SAT improvement of the students using the premium package will be at least

double the average SAT improvement of students using the standard package.

3. Suppose the company is lying and that the premium package actually has the same improvement as the standard

package. What would be the probability that the average SAT improvement of the students using the premium

package is higher than the average SAT improvement of students using the standard package