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The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 228...

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Statistics

The Downtown Parking Authority of Tampa, Florida, reported thefollowing information for a sample of 228 customers on the numberof hours cars are parked and the amount they are charged.

Number ofHoursFrequencyAmount Charged
121$4
2366
3539
44013
52214
61116
7918
83622
228


Click here for the Excel Data File

a-1. Convert the information on the number ofhours parked to a probability distribution. (Round youranswers to 3 decimal places.)

a-2. Is this a discrete or a continuousprobability distribution?

Discrete

Continuous

b-1. Find the mean and the standard deviationof the number of hours parked. (Do not round theintermediate calculations. Round your final answers to 3 decimalplaces.)

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

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

rev: 10_12_2018_QC_CS-142885

Answer & Explanation Solved by verified expert
3.9 Ratings (753 Votes)

a-1)

x P(x)
1 0.092
2 0.158
3 0.232
4 0.175
5 0.096
6 0.048
7 0.039
8 0.158

a-2) Discrete

b-1)

x P(x) xP(x) x2*P(x)
1 0.092 0.092 0.092
2 0.158 0.316 0.632
3 0.232 0.696 2.088
4 0.175 0.700 2.800
5 0.096 0.480 2.400
6 0.048 0.288 1.728
7 0.039 0.273 1.911
8 0.158 1.264 10.112
4.109 21.763
E(x) =μ= ΣxP(x) = 4.109
E(x2) = Σx2P(x) = 21.763
Var(x)=σ2 = E(x2)-(E(x))2= 4.879
std deviation=         σ= √σ2 = 2.209

mean =4.109

std deviation =2.209

b-2)

How long is a typical customer parked =4.109

c)

x P(x) xP(x) x2*P(x)
4 0.092 0.368 1.472
6 0.158 0.948 5.688
9 0.232 2.088 18.792
13 0.175 2.275 29.575
14 0.096 1.344 18.816
16 0.048 0.768 12.288
18 0.039 0.702 12.636
22 0.158 3.476 76.472
11.969 175.739
E(x) =μ= ΣxP(x) = 11.969
E(x2) = Σx2P(x) = 175.739
Var(x)=σ2 = E(x2)-(E(x))2= 32.482
std deviation=         σ= √σ2 = 5.699

mean =11.969

std deviation =5.699
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