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 | 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 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.)
Solutions
Expert Solution
(a- 1)
The information on the number of hours parked is converted to a probability distribution as follows:
| Number of hours (x) | Probability (p) |
| 1 | 22/232 = 0.095 |
| 2 | 38/232 = 0.164 |
| 3 | 50/232 = 0.216 |
| 4 | 45/232 = 0.194 |
| 5 | 20/232 = 0.086 |
| 6 | 16/232 = 0.069 |
| 7 | 5/232 = 0.022 |
| 8 | 36/232 = 0.154 |
(a - 2)
Discrete
(b - 1)
From the probability distribution, the following Table, calculated:
| Number of hours (x) | Probability (p) | p.x | p.x2 |
| 1 | 0.095 | 0.095 | 0.095 |
| 2 | 0.164 | 0.328 | 0.656 |
| 3 | 0.216 | 0.648 | 1.944 |
| 4 | 0.194 | 0.776 | 3.104 |
| 5 | 0.086 | 0.430 | 2.150 |
| 6 | 0.069 | 0.414 | 2.484 |
| 7 | 0.022 | 0.154 | 1.078 |
| 8 | 0.154 | 1.232 | 9.856 |
| Total |  |
 |
(i)
the mean of the number of hours parked. =
(ii)
the standard deviation of the number of hours parked. 
(b - 2)
The number of hours a typical customer parked =
(c)
n = 8
| x | (x - 
) |
(x -
)2 |
| 2 | - 10.25 | 105.0625 |
| 6 | - 6.25 | 39.0625 |
| 8 | - 4.25 | 18.0625 |
| 12 | - 0.25 | 0.0625 |
| 14 | 1.75 | 3.0625 |
| 16 | 3.75 | 14.0625 |
| 18 | 5.75 | 33.0625 |
| 22 | 9.75 | 95.0625 |
| Total = | 307.5 |
Standard Deviation (s) is given by:
So, answer is:
the mean of the amount charged. : 12.250
the standard deviation of the amount charged. 6.628
orchestra answered 2 years 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
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...
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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