Question

The parking authority in downtown Halifax reported the following information for a sample of 240 customers on the number of hours cars are parked and the amount they are charged: Number of Hours Frequency Amount Charged 1 23 $2 2 41 4 3 54 6 4 41 8 5 38 10 6 11 14 7 6 18 8 26 20 Total 240 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? 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

Number of hours	Frequency	Amount charged
1	23	2
2	41	4
3	54	6
4	41	8
5	38	10
6	11	14
7	6	18
8	26	20
	240

a)

Number of hours	p
1	0.095833
2	0.170833
3	0.225
4	0.170833
5	0.158333
6	0.045833
7	0.025
8	0.108333

this is discrete

b)

Number of hours	p	xp	x^2p
1	0.0958	0.0958	0.0958
2	0.1708	0.3417	0.6833
3	0.2250	0.6750	2.0250
4	0.1708	0.6833	2.7333
5	0.1583	0.7917	3.9583
6	0.0458	0.2750	1.6500
7	0.0250	0.1750	1.2250
8	0.1083	0.8667	6.9333
	1.0000	3.9042	19.3042

mean = 3.904

sd =sqrt(E(X^2) - (E(X))^2)

=sqrt(19.3042 -3.9042^2)

= 2.01529

=2.015

b-2)

typical number of hours = mean = 3.904

c)

Amount charged	p	xp	x^2p
2	0.0958	0.1917	0.3833
4	0.1708	0.6833	2.7333
6	0.2250	1.3500	8.1000
8	0.1708	1.3667	10.9333
10	0.1583	1.5833	15.8333
14	0.0458	0.6417	8.9833
18	0.0250	0.4500	8.1000
20	0.1083	2.1667	43.3333
	1.0000	8.4333	98.4000

mean = 8.433

sd = sqrt(98.4 - 8.4333^2)

= 5.223

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