Question

QUESTION 3

Jay –Ethan Company is a multi-billion pharmaceutical company that has won a contract by the government to produce hand sanitizers and respiratory gadgets for frontline health workers in Bono East region. As a result, the company has decided to give bonuses to its employees to motivate them for the risky task ahead. A sample of the weekly bonus received by the employees is organized in the table below:

Weekly Bonus ($)	30<35	35<40	40<45	45<50	50<55	55<60	60<56	65<70
Number of employees(f)	8	6	10	5	15	4	9	3

NB: Approximate to 2 decimal places

i) Find the mean amount of bonus given to the employees                                         ii) Calculate the standard deviation and interpret it.  

                                                    iii) What is the modal amount paid?                                                                              iv) Would you say the bonus distribution follows the standard normal distribution? Why?     

                                                                                                                                 

v)        Calculate the coefficient of variation for the bonus distribution of Jay-Ethan and compare it with the coefficient of variation of 19.45% for the bonus distribution of KGH, a subsidiary of Jay-Ethan.

                                                                                                                               

                                                                                                                                       

Answer 1

WEEKLY BONUS($)

NUMBER OF EMPLOYEES()

30-35	8	32.5	260	8450
35-40	6	37.5	225	8437.5
40-45	10	42.5	425	18062.5
45-50	5	47.5	237.5	11281.25
50-55	15	52.5	787.5	41343.75
55-60	4	57.5	230	13225
60-65	9	62.5	562.5	35156.25
65-70	3	67.5	202.5	13668.75

is the midpoint of the class which we get by adding the class limits and divide by 2.

(1)To find mean

is  the mean amount of bonus given to the employees .

(2)Standard Deviation

First find Variance

Standard deviation

=10.53(approximate to two decimal places)

The standard deviation measures how concentrated the data are around the mean

The more concentrated, the smaller the standard deviation.In situations where the results are restricted, a small standard deviation can be a goal.

(3) Modal amount

Where

i = class width (5)

difference between frequency of class mode and frequency of class after the class mode (15-5=10)

difference between frequency of class mode and frequency of class before the class mode (15-4=11)

lower boundary of class mode (50)

is the modal amount paid.

(4) The standard normal distributiondistribution that occurs when a normal random variable has a mean of 0 and a standard deviation of 1.Since the mean and standard deviation of this data doesnt fall in the said category, the bonus distribution in this case is not Standard normal distribution.