Question
In: Statistics and Probability
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 232...
|
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 | 20 | $ | 3 | |||
| 2 | 37 | 7 | ||||
| 3 | 49 | 10 | ||||
| 4 | 39 | 17 | ||||
| 5 | 33 | 21 | ||||
| 6 | 17 | 25 | ||||
| 7 | 3 | 27 | ||||
| 8 | 34 | 31 | ||||
| 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 | |
Solutions
Expert Solution
a-1)
The probability is for each number of hour is obtained by dividing the frequency by total frequency,
| Number of Hours | Frequency | Probability |
| 1 | 20 | 20/232=0.086 |
| 2 | 37 | 37/232=0.159 |
| 3 | 49 | 49/232=0.211 |
| 4 | 39 | 39/232=0.168 |
| 5 | 33 | 33/232=0.142 |
| 6 | 17 | 17/232=0.073 |
| 7 | 3 | 3/232=0.013 |
| 8 | 34 | 34/232=0.147 |
| Total | 232 |
a-2)
Answer: discrete
Explanation: Since we calculating the probability for discrete data (frequency), this is a discrete probability distribution.
b-1)
The mean for the the number of hours parked is obtained using the formula,
| Number of Hours, x | Frequency, f |
 |
| 1 | 20 | 20 |
| 2 | 37 | 74 |
| 3 | 49 | 147 |
| 4 | 39 | 156 |
| 5 | 33 | 165 |
| 6 | 17 | 102 |
| 7 | 3 | 21 |
| 8 | 34 | 272 |
| Total | 232 | 957 |
The standard deviation for the number of hours parked is obtained using the formula,
| Number of Hours, x | Frequency, f |
 |
 |
 |
| 1 | 20 | -3.125 | 9.766 | 195.313 |
| 2 | 37 | -2.125 | 4.516 | 167.078 |
| 3 | 49 | -1.125 | 1.266 | 62.016 |
| 4 | 39 | -0.125 | 0.016 | 0.609 |
| 5 | 33 | 0.875 | 0.766 | 25.266 |
| 6 | 17 | 1.875 | 3.516 | 59.766 |
| 7 | 3 | 2.875 | 8.266 | 24.797 |
| 8 | 34 | 3.875 | 15.016 | 510.531 |
| Total | 232 | 1045.375 |
b-2)
A typical customer parked with mean value = 4.125 hours.
c)
The mean for the amount charged is,
| Amount Charged | Frequency, f |
|
| 3 | 20 | 60 |
| 7 | 37 | 259 |
| 10 | 49 | 490 |
| 17 | 39 | 663 |
| 21 | 33 | 693 |
| 25 | 17 | 425 |
| 27 | 3 | 81 |
| 31 | 34 | 1054 |
| Total | 232 | 3725 |
The standard deviation for the amount charged is,
| Amount Charged | Frequency, f |
|
|
|
| 3 | 20 | -13.056 | 170.460 | 3409.201 |
| 7 | 37 | -9.05603 | 82.012 | 3034.435 |
| 10 | 49 | -6.05603 | 36.676 | 1797.102 |
| 17 | 39 | 0.943966 | 0.891 | 34.752 |
| 21 | 33 | 4.943966 | 24.443 | 806.612 |
| 25 | 17 | 8.943966 | 79.995 | 1359.907 |
| 27 | 3 | 10.94397 | 119.770 | 359.311 |
| 31 | 34 | 14.94397 | 223.322 | 7592.952 |
| Total | 232 | 18394.272 |
orchestra answered 1 year agoRelated Solutions
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 232...
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
22
$
2
2
38
6
3
50
8
4
45
12
5
20
14
6
16
16
7
5
18
8
36
22
232
Click here for the Excel Data File
a-1. Convert the information on the number of hours parked...
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 231...
The Downtown Parking Authority of Tampa, Florida, reported the
following information for a sample of 231 customers on the number
of hours cars are parked and the amount they are charged.
Number of
Hours
Frequency
Amount Charged
1
22
$
3
2
38
6
3
51
8
4
45
12
5
20
14
6
14
16
7
5
18
8
36
22
231
Click here for the Excel Data File
a-1. Convert the information on the number of
hours parked...
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 231...
The Downtown Parking Authority of Tampa, Florida, reported the
following information for a sample of 231 customers on the number
of hours cars are parked and the amount they are charged.
Number of Hours
Frequency
Amount Charged
1
22
$
3
2
38
6
3
51
8
4
45
12
5
20
14
6
14
16
7
5
18
8
36
22
231
a-2. Is this a discrete or a continuous
probability distribution?
b-1. Find the mean and the standard...
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 231...
The Downtown Parking Authority of Tampa, Florida, reported the
following information for a sample of 231 customers on the number
of hours cars are parked and the amount they are charged.
Number of Hours
Frequency
Amount Charged
1
22
$
3
2
38
6
3
51
8
4
45
12
5
20
14
6
14
16
7
5
18
8
36
22
231
b-1. Find the mean and the standard deviation
of the number of hours parked
b-2. How long...
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 236...
The Downtown Parking Authority of Tampa, Florida, reported the
following information for a sample of 236 customers on the number
of hours cars are parked and the amount they are charged.
Number of
Hours
Frequency
Amount Charged
1
25
$
3
2
42
7
3
53
9
4
40
12
5
20
14
6
11
17
7
9
19
8
36
22
236
Click here for the Excel Data File
a-1. Convert the information on the number of
hours parked...
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 230...
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 Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 235...
The Downtown Parking Authority of Tampa, Florida, reported the
following information for a sample of 235 customers on the number
of hours cars are parked and the amount they are charged.
Number of Hours
Frequency
Amount Charged
1
25
$
2
2
40
5
3
52
8
4
45
12
5
20
5
6
12
18
7
5
20
8
36
22
235
Click here for the Excel Data File
a-1. Convert the information on the number of
hours parked...
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 231...
The Downtown Parking Authority of Tampa, Florida, reported the
following information for a sample of 231 customers on the number
of hours cars are parked and the amount they are charged.
Number of Hours
Frequency
Amount Charged
1
22
$
3
2
38
6
3
51
8
4
45
12
5
20
14
6
14
16
7
5
18
8
36
22
231
a-1. Convert the information on the number of
hours parked to a probability distribution. (Round your
answers...
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 231...
The Downtown Parking Authority of Tampa, Florida, reported the
following information for a sample of 231 customers on the number
of hours cars are parked and the amount they are charged.
Number of Hours
Frequency
Amount Charged
1
19
$
3
2
35
8
3
48
13
4
42
16
5
35
20
6
16
24
7
5
27
8
31
30
231
Find the mean and the standard deviation of the number of hours
parked. (Do not...
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 228...
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...
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