Question

Erin Examinator is an educational researcher that has created an exam to measure the football knowledge of students across the nation.  She has decided to focus her research on students at the University of Alabama, as she believes that have a high level of football knowledge.  In her previous work, she has determined that the nationwide average for her exam is 65 (µ = 65) with a standard deviation equal to 12 (σ = 12).  Assume the data are normally distributed. Use this information to answer parts a-i.

1. (6 points) Freddy Footballer is not an average college student, he is over the top when it comes to his football knowledge.  Erin is very interested in seeing how Freddy compared to the national average.  Freddy scored a 99 (X = 99) on the exam.  Find the probability that she can find a student that scored higher than him. That is: P(X > 99).

2. b) (2 points) What is the probability that Erin will find a student that scored exactly 91? (X = 91)

3. (5 points) What is the percentile score of Freddy’s cousin, Frank Footballer? (His X = 92)

4. (7 points) Erin is interested in determining if any of the students that attended last week’s football game were below the 80^thpercentile of scores on the exam.  In order to do that, she needs to find the exam score, X, that falls in the 80^thpercentile.  Find that score for her.  

Note: (µ = 65) and (σ = 12).  

5. e. (8 points) Erin then samples 35 students (n = 35) that attended the game on Saturday that were seated in the student section.  She wants to determine if the students in this section are more knowledgeable than other students attending the games.  She finds the sample mean of this sample of students to be 72 .  Find the percentile score for mean of the students from the student section.   Note: (µ = 65) and (σ = 12).  

6. f. (6 points)  Now help Erin find the mean score,  , that falls in the 75^thpercentile of exam scores for the same sample size.  Note:  (µ = 65), (σ = 12) and (n = 35).     

7. (10 points) Help Erin to better estimate the true mean knowledge score of students from the University of Alabama.  Find a 99% Confidence Interval for true mean based on the 35 students (n = 35). Interpret the confidence interval.  Note:  and (σ = 12).  

8. (5 points) Erin is a perfectionist and wants to estimate the true mean within 1 point (E = 1).  Find the sample size she would need to collect in order to reduce the error to 1 in her 99% confidence interval.  Note: (σ = 12).  

1.   (10 points) Erin’s assistant, Abbie Assister, decides she would like to learn how to estimate the sample mean.  For practice, she collects data from 12 students (n = 12) and the sample mean was  and a sample standard deviation equal to (s = 9.87).  Find the 95% confidence interval for this sample mean and interpret the interval.  

Answer 1

I HOPE ITS HELPFULL TO YOU...IF YOU HAVE ANY DOUBTS PLS COMMENTS BELOW....I WILL BE THERE TO HELP YOU....PLS RATE THUMBS UP........!!

AS FOR GIVEN DATA....

I HOPE YOU UNDERSTAND...

PLS RATE THUMBS UP...ITS HELPS ME ALOT....

THANK YOU...!!