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Step 1: Hand calculation Assignment • Make sure to include answers on a word document • And any calculations as a jpeg or pdf file A large university administers entrance exams to all entering students. The test is administered again as an exit exam for all graduates. The test results for one group of students are given below. Freshman Year • Mean = 53 • sd = 7 Senior Year • Mean = 92 • sd = 4 The scores for three students on both tests are listed below. For each student calculate Z scores and determine whether the student performed better as a freshman or as a senior. Student A • Freshman score - 57 Senior score - 97 Student B • Freshman score - 51 Senior score - 94 Student C • Freshman score - 45 Senior score - 82 Determine the probabilities that randomly selected students will have scores in each of these ranges As a freshman • Less than 52 • Between 40 and 50 • More than 62

          Step 1: Hand calculation Assignment
• Make sure to include answers on a word document
• And any calculations as a jpeg or pdf file
A large university administers entrance exams to all entering students. The test is administered again as an exit exam for all graduates. The test results for one group of students are given below.
Freshman Year
• Mean = 53
• sd = 7
Senior Year
• Mean = 92
• sd = 4
The scores for three students on both tests are listed below. For each student calculate Z scores and determine whether the student performed better as a freshman or as a senior.
Student A
• Freshman score - 57 Senior score - 97
Student B
• Freshman score - 51 Senior score - 94
Student C
• Freshman score - 45 Senior score - 82
Determine the probabilities that randomly selected students will have scores in each of these ranges
As a freshman
• Less than 52
• Between 40 and 50
• More than 62

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Step 1: Hand calculation Assignment
• Make sure to include answers on a word document
• And any calculations as a jpeg or pdf file
A large university administers entrance exams to all entering students. The test is administered again as an exit exam for all graduates. The test results for one group of students are given below.
Freshman Year
• Mean = 53
• sd = 7
Senior Year
• Mean = 92
• sd = 4
The scores for three students on both tests are listed below. For each student calculate Z scores and determine whether the student performed better as a freshman or as a senior.
Student A
• Freshman score - 57 Senior score - 97
Student B
• Freshman score - 51 Senior score - 94
Student C
• Freshman score - 45 Senior score - 82
Determine the probabilities that randomly selected students will have scores in each of these ranges
As a freshman
• Less than 52
• Between 40 and 50
• More than 62

Added by C S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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A large university administers entrance exams to all entering students. The test is administered again as an exit exam for all graduates. The test results for one group of students are given below. Freshman Year Mean = 53 sd = 7 Senior Year Mean = 92 sd = 4 The scores for three students on both tests are listed below. For each student calculate Z scores and determine whether the student performed better as a freshman or as a senior. Student A Freshman score - 57 Senior score - 97 Student B Freshman score - 51 Senior score - 94 Student C Freshman score - 45 Senior score - 82 Determine the probabilities that randomly selected students will have scores in each of these ranges As a freshman Less than 52 Between 40 and 50 More than 62 As a senior Less than 98 Between 80 and 100 More than 85

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Transcript

00:01 So for the standard scores, we want to see which students did better as a freshman or senior, and we're going to do that by standardizing these with the z -score.

00:10 Z is going to be our data point minus the mean over our standard deviation.

00:14 So for the freshman scores, i'm going to go 57 minus 53 over 7, 51 minus 53 over 7, 45 minus 53 over 7.

00:27 For the senior scores, i'll go 97 minus 92 over 4, 94 minus 92 over 4, and 82 minus 92 over 4.

00:39 So i'm going to go ahead and do some of these.

00:41 That's going to be 5 over 4, which is 1 .25.

00:45 This is going to be 2 over 4, which is 1 half or 0 .5.

00:49 This is going to be negative 10 over 4, which will be negative 2 .25.

00:54 Now these i can't do in my head, so this is going to be 4 sevenths, which is going to be 0 .57.

01:03 Here we're going to have negative 2 sevenths, which is going to be negative 0 .29, and then here we're going to have negative 8 sevenths, which is going to be negative 8 sevenths is going to equal to negative 1 .14.

01:24 So the one with the higher z score is the one that they did better.

01:28 So for a, they did better as a senior.

01:32 For b, they did better as a senior.

01:35 For c, they did better as a freshman.

01:37 So now we want to know the probability that the following ranges as a score as a freshman, and we want these particular values.

01:48 Let me get my pen here.

01:50 We're doing freshmen, so we need less than 52 between 40 and 60, and then more than 62.

01:59 So we need to find the z scores for 52, 60, and 64, 52, 40, 60, and 62.

02:08 So we're going to do it the same way we did here.

02:10 52 minus 53, that's going to be negative 1 divided by 7...

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