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 in the table.
Freshman Year  Senior Year 




a. The scores for five students on both tests are listed below. For each student, calculate
Student  Score, Freshman Year  Score, Senior Year 
A  57  97 
B  51  94 
C  45  82 
D  73  101 
E  62  98 
b. Determine the probabilities that randomly selected students will have scores in each of these ranges:
Freshman Year  
Score  Probability 
Less than 52  
Less than 57  
Between 40 and 50  
More than 51  
More than 62 
Senior Year  
Score  Probability 
Less than 88  
Less than 98  
Between 80 and 100  
More than 97  
More than 85 
(a)
To find:
The
Given:
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 in the table below,
Freshman Year  Senior Year 
Description:
The normal curve is symmetrical and its mean is equal to the median. The area below and above the mean is 50% or 0.05.
Formula used:
Let the data values be denoted by
The formula to calculate the
Where,
Calculation:
Given that for freshmen year the mean is 53 and standard deviation is 7.
For the score of 57,
Substitute 57 for
For the score of 51,
Substitute 51 for
For the score of 45,
Substitute 45 for
For the score of 73,
Substitute 73 for
For the score of 62,
Substitute 62 for
Given that for senior year the mean is 92 and standard deviation is 4.
For the score of 97,
Substitute 97 for
(b)
To find:
The probabilities of the given ranges.
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Applied Calculus
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: An Applied Approach (MindTap Course List)
Multivariable Calculus
Calculus: Early Transcendentals
Calculus: Early Transcendental Functions
Finite Mathematics and Applied Calculus (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Statistics for The Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
Understanding Basic Statistics
Probability and Statistics for Engineering and the Sciences
Finite Mathematics
Single Variable Calculus
Intermediate Algebra
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Contemporary Mathematics for Business & Consumers
Elementary Technical Mathematics
Mathematical Excursions (MindTap Course List)
Elements Of Modern Algebra
Elementary Geometry For College Students, 7e
Trigonometry (MindTap Course List)
Mathematical Applications for the Management, Life, and Social Sciences
Finite Mathematics for the Managerial, Life, and Social Sciences
Calculus of a Single Variable
Single Variable Calculus: Early Transcendentals
Calculus: Early Transcendental Functions (MindTap Course List)
Introduction To Statistics And Data Analysis
Elementary Geometry for College Students
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Multivariable Calculus, 8th
Research Methods for the Behavioral Sciences (MindTap Course List)
STATISTICS F/BUSINESS+ECONOMICSTEXT
Statistics for Business & Economics, Revised (MindTap Course List)
Research Methods for the Behavioral Sciences (MindTap Course List)
Mathematics For Machine Technology
College Algebra (MindTap Course List)
Calculus (MindTap Course List)
Multivariable Calculus
Essentials Of Statistics For Business & Economics
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Discrete Mathematics With Applications
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Mathematics: A Practical Odyssey
Introductory Statistics
Calculus Volume 1
Calculus Volume 2
College Algebra
A First Course in Differential Equations with Modeling Applications (MindTap Course List)