Question

Cars arrive at Carla’s Muffler Shop for repair work at an average of 3 per hour, following an exponential distribution. (a) What is the expected time between arrivals? (b) What is the variance of the time between arrivals?

Use Appendix C

Answer 1

Formula sheet

A	B	C	D	E	F	G
2
3		Exponential Distribution function is given by following formula:
4
5		f(x) = ?e-?x
6
7		Where:
8		?: The rate parameter of the distribution, = 1/µ (Mean)
9		f(x): Exponential probability density function
10		x: Random variable
11
12		Mean of exponential function	=1/?
13		Variance of exponential function	=1/?2
14
15		Since ? is the rate parameter, car arriving at the rate of 3 per hour is ?.
16		?=	3	Per hour
17
18		a)
19
20		Expected time between arrival	=Mean of exponential distribution
21			=1/ ?
22			=1/D16	hours
23			=D22*60	min
24
25		Hence Expected time between arrival	=D23	min
26
27		b)
28
29		Variance of exponential function	=1/?2
30			=1/(D16^2)	=1/(D16^2)
31
32		Hence Variance of time between arrival is	=D30
33