Suppose that the average time an employee takes to reach the

Suppose that the average time an employee takes to reach the office is 35 minutes. To address the issue of late comers, the mode of transport chosen by the employee is tracked: private transport (two-wheelers and four-wheelers) and public transport. The data on the average time (in minutes) taken using both a private transportation system and a public transportation system for a sample of employees are given below:

Private Transport

Public Transport

27

30

33

29

28

25

32

20

20

27

34

32

30

37

28

38

18

21

29

35

a. Considering the travel times (in minutes) of employees using private transport. Compute the z-score for the tenth employee with travel time of 29 minutes.

b. Considering the travel times (in minutes) of employees using public transport. Compute the z-score for the second employee with travel time of 29 minutes. How does this z-score compare with the z-score you calculated for part a?
c. Based on z-scores, do the data for employees using private transport and public transport contain any outliers? Show all work to support your answer.

Solution

to check the z score we have to find the mean and the standard deviation of both the groups seperately

private transport

mean = sum of all / total number = 279/10 = 27.9

standard deviation =

hence standard dev = 5.23

A) z score = (29 - 27.9)/5.23 = 0.21

z score = 0.5832

b) public transport

mean = 294/10 = 29.4

standard dev = 6.27

z score = (29-29.4)/6.27 = -0.06

z score = 0.5239

c) outlier is the number which is too deviation either high or low fromthe rest numbers

in private the number is 18

in public no outlier,