Answer to Question #259581 in Statistics and Probability for Bros

Question

a)     Mzee Kobe Bank wished to establish the times in seconds that each ATM transaction takes. A sample of ATM users were observed and the time in seconds each spent at the ATM was as follows:

Time (seconds)

10-19

20-29

30-39

40-49

50-59

Number of customer

15

60

67

98

2

 

i.                    Calculate the coefficent of variation of the waiting time? ( 6 marks)

Answer 1

Sample mean

mx=$\frac{14.5\cdot 15+24.5\cdot 60+34.5\cdot 67+44.5\cdot 98+54.5\cdot 2} {15+60+67+98+2}=35$

Sample variance

Var(x)=$\frac{(14.5-35)^2\cdot 15+(24.5-35)^2\cdot 60+(34.5-35)^2\cdot 67+(44.5-35)^2\cdot 98+(54.5-3)^2\cdot 2} {242}=93.143$

Var(x)=93.143- variance of waiting time

Standard deviation

$\sigma=\sqrt{Var(x)}=\sqrt{93.143}=9.651$

Coefficent of variation

$CV(x)=\frac{\sigma(x)}{mx}=\frac{9.651}{35}=0.276=27.6$ %