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? |
|
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 :
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
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