Question

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 232 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		36			8
3		51			14
4		41			17
5		37			22
6		12			24
7		6			26
8		34			30
		232

a.	Convert the information on the number of hours parked to a probability distribution. (Round your 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?
	Continuous Discrete

b-1.	Find the mean and the standard deviation of the number of hours parked. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)

Mean
Standard deviation

b-2.	How long is a typical customer parked? (Do not round intermediate calculations. Round your final answers to 3 decimal places.)

The typical customer is parked for

hours

c.	Find the mean and the standard deviation of the amount charged. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)

Mean
Standard deviation

Answer 1

Answer :

Given data is :

Sample size = n = 232

a)1)No.of hours packed = X

Probability of relative frequency = P = f / n

Where f = frequency

n = Total frequency

The table becomes as follows :

X(Hours)	Frequency(f)	Probability= P(X)
1	15	= 15 / 232 = 0.0647
2	36	= 36 / 232 = 0.1552
3	51	= 51 / 232 = 0.2198
4	41	= 41 / 232 = 0.1767
5	37	= 37 / 232 = 0.1595
6	12	= 12 / 232 = 0.0517
7	6	= 6 / 232 = 0.0259
8	34	= 34 / 232 = 0.1466
		P(X) = 1.000

Total number of probability = P(X) = 1.000

a)2)This is discrete probability distribution.Because we calculated the number of hours are packed in discrete.

b)1)Here we need to calculate mean and standard deviation.

Mean =

= 1(0.0647) + 2(0.1552) + 3(0.2198) + 4(0.1767) + 5(0.1595) + 6(0.0517) + 7(0.0259) + 8(0.1466)

= 0.0647 + 0.3104 + 0.6594 + 0.7068 + 0.7975 + 0.3102 + 0.1813 + 1.1728

= 4.203

Mean = 4.203

Standard deviation =

Standard deviation = 2.080

b)2)typical customer parked in 4.203 hours

c)Given amount charged is :

X

2

8

14

17

22

24

26

30

P(X) we already calculated in above bits.

Mean =

Standard deviation =

Standard deviation = 7.901