Question

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 230 customers on the number of hours cars are parked and the amount they are charged.

Number of Hours		Frequency		Amount Charged
1		22		$	4
2		38			6
3		52			8
4		45			12
5		20			14
6		12			16
7		5			18
8		36			22
		230

Convert the information on the number of hours parked to a probability distribution.

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

How long is a typical customer parked? (Do not round the intermediate calculations. Round your final answer to 3 decimal places.)

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

Answer 1

for number of hours parked,

probability = f/N

X	P(X)	X*P(X)	X² * P(X)
1	0.096	0.096	0.0957
2	0.165	0.330	0.6609
3	0.226	0.678	2.0348
4	0.196	0.783	3.1304
5	0.087	0.435	2.1739
6	0.05	0.313	1.8783
7	0.02	0.152	1.0652
8	0.16	1.252	10.0174

	P(X)	X*P(X)	X² * P(X)
total sum =	1	4.03913	21.06

mean = E[X] = Σx*P(X) =            4.039
          
E [ X² ] = ΣX² * P(X) =            21.0565
          
variance = E[ X² ] - (E[ X ])² =            4.7419
          
std dev = √(variance) =            2.178

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4.039 hours  is a typical customer parked

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for  the amount charged

X	P(X)	X*P(X)	X² * P(X)
4	0.096	0.383	1.5304
6	0.165	0.991	5.9478
8	0.226	1.809	14.4696
12	0.196	2.348	28.1739
14	0.087	1.217	17.0435
16	0.05	0.835	13.3565
18	0.02	0.391	7.0435
22	0.16	3.443	75.7565

	P(X)	X*P(X)	X² * P(X)
total sum =	1	11.41739	163.32

mean = E[X] = Σx*P(X) =            11.417
          
E [ X² ] = ΣX² * P(X) =            163.3217
          
variance = E[ X² ] - (E[ X ])² =            32.9649
          
std dev = √(variance) =            5.742