In: Statistics and Probability
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 228 customers on the number of hours cars are parked and the amount they are charged.
| Number of Hours | Frequency | Amount Charged | |||
| 1 | 21 | $ | 4 | ||
| 2 | 36 | 6 | |||
| 3 | 53 | 9 | |||
| 4 | 40 | 13 | |||
| 5 | 22 | 14 | |||
| 6 | 11 | 16 | |||
| 7 | 9 | 18 | |||
| 8 | 36 | 22 | |||
| 228 | |||||
Click here for the Excel Data File
a-1. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)
a-2. Is this a discrete or a continuous probability distribution?
Discrete
Continuous
b-1. 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.)
b-2. 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.)
rev: 10_12_2018_QC_CS-142885
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