MGSC2301 PROJECT #2 (Probability Distributions) complete solutions correct answers key

MGSC2301 PROJECT #2 (Probability Distributions) complete solutions correct answers key

This project also utilizes the data set for the Bank and Trust Company (B&T); the random sample of 222 employees and data recorded for several variables:

·         Annual salary earned by the employee; 

·         The age of the employee;

·         The years of experience in the banking industry held by the employee prior to

           joining B&T;

·         The education level of the employee;

·         The extent to which the employee uses a computer;

·         The grade classification within B&T held by the employee;

·         The years of experience at B&T;

·         The gender of the employee;

·         The citizenship of the employee; and

·         A cost-of-living indicator based on location.

Assume that you still work for Ms. Deanna V. Ashun and that the lawsuit alleging gender bias is still a concern at B&T.  Ms. Ashun has asked you to complete several tabulations and calculations, excluding the CEO from all these calculations.

(a)     Find the average salary for all employees in the sample (remember to exclude the CEO).

          Please round your answer to the nearest $1000.

           (4 points)

(b)      Recode the salary data in the sample into one of two categories:

           ·         Greater than or equal to the average salary (to the nearest $1000)

·          Below the average salary (to the nearest $1000)

Then create a two-by-two (contingency) table, using gender and salary as the row and column headings.

(6 points)

(c)      After reading your legal brief from Project 1, Ms. Ashun is concerned that B&T may have some liability concerning promotion practices.  Specifically, she wonders if female branch managers are getting promoted as frequently as male branch managers.  She decides to start the analysis by looking at their salaries, and asks you to consider those individuals in GRADE 4 (branch managers).   For these individuals, again find the average salary, round this to the nearest $1000, and redo the table from part (b).

           (10 points)

(d)     If a person in GRADE 4 were selected at random, what is the probability that this individual would be both female and earn an annual salary greater than or equal to the average found in part (c)?

          (9 points)

(e)      Assume the probability found in part (d) holds for all B&T employees.  That is, you are willing to assume that P(Female Ç Salary ³ Average) does not change from employee to employee.  At this point, Ms. Ashun informs you that she is enlarging her sample, and more B&T employees are randomly selected and added to the data base.  Of these, 10 were in GRADE 4.

e1.     What is the probability that fewer than half of these 10 new individuals will be both female and earn a salary greater than or equal to the average for GRADE 4?

                 (7 points)

e2.     What is the probability that exactly half of these 10 new individuals will be both female and earn a salary greater than or equal to the average for GRADE 4?

                (7 points)

e3.     What is the probability that half or grater of these 10 new individuals will be both female and earn a salary greater than or equal to the average for GRADE 4?

                (7 points)

NAME(s):               ______________________________________

                                ______________________________________

                                ______________________________________

SCORE (out of 50):                    __________________________

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

           _

(a)      XSALARY = $ _____________________________________  (to nearest $1000)

(b)      Please complete the table below:

Gender

SALARY

TOTAL

Below average

Above or equal to average

Female

Male

TOTAL

           _

(c)       XSALARY(GRADE 4) = $ ______________________________ (to nearest $1000)

MGSC2301                    YELLOW SHEET FOR:   PROJECT. #2           Page 2

Please complete the table below:

Gender

SALARY

TOTAL

Below average

Above or equal to average

Female

Male

TOTAL

(d)     P(Female Ç Salary ³ Average | GRADE 4) = __________________

(e)      e1.       P(less than half of new 10 will be

    female and earn ³ average salary) = ___________________

          e2.       P(exactly half of 10 will be female

    and earn ³ average salary) = _________________________

e3.       P(half or grater of 10 will be female

    and earn ³ average salary) = _________________________