Question

The parking authority in downtown Halifax reported the following information for a sample of 260 customers on the number of hours cars are parked and the amount they are charged:

Number of Hours	Frequency	Amount Charged
1	15	$2
2	44	4
3	63	6
4	49	8
5	38	10
6	13	14
7	7	18
8	31	20
Total	260

a-1. Convert the information on the number of hours parked to a probability distribution. (Round the final answers to 3 decimal places.)

Hours	Probability
1
2
3
4
5
6
7
8

a-2. Is this a discrete or a continuous probability distribution?

(Click to select)  Discrete  Continuous

b-1. Find the mean and the standard deviation of the number of hours parked. (Round the final answers to 3 decimal places.)

Mean            

Standard deviation            

b-2. How would you answer the question, how long is a typical customer parked? (Round the final answer to 3 decimal places.)

The typical customer is parked for  hours.

c. Find the mean and standard deviation of the amount charged. (Round the final answers to 2 decimal places.)

Mean            

Standard deviation            

Answer 1

a-1) dividing each value with 260

x	P(x)	xP(x)	x2*P(x)
1	0.058	0.058	0.058
2	0.169	0.338	0.676
3	0.242	0.726	2.178
4	0.188	0.752	3.008
5	0.146	0.730	3.650
6	0.050	0.300	1.800
7	0.027	0.189	1.323
8	0.119	0.952	7.616
		4.045	20.309
E(x) =μ=	ΣxP(x) =		4.045
E(x2) =	Σx2P(x) =		20.309
Var(x)=σ2 =	E(x2)-(E(x))2=		3.947
std deviation=	σ= √σ2 =		1.987

a-2) discrete

b-1)

x	P(x)	xP(x)	x2*P(x)
1	0.058	0.058	0.058
2	0.169	0.338	0.676
3	0.242	0.726	2.178
4	0.188	0.752	3.008
5	0.146	0.730	3.650
6	0.050	0.300	1.800
7	0.027	0.189	1.323
8	0.119	0.952	7.616
		4.045	20.309
E(x) =μ=	ΣxP(x) =		4.045
E(x2) =	Σx2P(x) =		20.309
Var(x)=σ2 =	E(x2)-(E(x))2=		3.947
std deviation=	σ= √σ2 =		1.987

mean =4.045 (try 4.050 if this comes wrong)

stnadard deviation =1.987 (try 1.983 if this comes wrong)

b-2)

typical customer is parked for 4.045 (try 4.050 if this comes wrong)

c)

x	P(x)	xP(x)	x2*P(x)
2	0.058	0.116	0.232
4	0.169	0.676	2.704
6	0.242	1.452	8.712
8	0.188	1.504	12.032
10	0.146	1.460	14.600
14	0.050	0.700	9.800
18	0.027	0.486	8.748
20	0.119	2.380	47.600
		8.774	104.428
E(x) =μ=	ΣxP(x) =		8.774
E(x2) =	Σx2P(x) =		104.428
Var(x)=σ2 =	E(x2)-(E(x))2=		27.445
std deviation=	σ= √σ2 =		5.239

mean =8.774 (try 8.785 if this comes wrong)

stnadard deviation =5.239 (try 5.233 if this comes wrong)