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 est out the more expensive premium package. Assuming a normal distribution with a variance of 1600 for the grade mprovement of each package determine the following. 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 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. 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

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
An online SAT Test Prep company offers two packages to use their services: the Standard package, which they claim will improve a student's SAT score by an average of 40 points, and a Premium package, which 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?
Transcribed Image Text:An online SAT Test Prep company offers two packages to use their services: the Standard package, which they claim will improve a student's SAT score by an average of 40 points, and a Premium package, which 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?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman