The parking authority in downtown Halifax reported the following information for
ID: 3151376 • Letter: T
Question
The parking authority in downtown Halifax reported the following information for a sample of 250 customers on the number of hours cars are parked and the amount they are charged: Number of Hours Frequency Amount Charged
1 23 $2
2 40 5
3 50 8
4 45 10
5 37 12
6 13 15
7 4 18
8 38 20
Total 250
a-1. Convert the information on the number of hours parked to a probability distribution. (Round the final answers to 3 decimal places.)
Hours
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. (Round the final answer to 3 decimal places.)
b-2. How would you answer the question, how long is a typical customer parked? (Round the final answer to 3 decimal places.)
c. Find the mean and standard deviation of the amount charged. (Round the final answer to 2 decimal places.)
Explanation / Answer
a-1.
We simply divide each frequency by 250,
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a-2.
As x can only take integer values, it is DISCRETE. [ANSWER]
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b-1.
Consider:
Thus,
E(x) = mean = Sum(xP(x)) = 4.112 [ANSWER]
Also,
Var(x) = E(x^2) - E(x)^2 = 4.587456
s(x) = sqrt [Var(x)] = 2.141834728 [ANSWER, STANDARD DEVIATION]
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b-2.
We give him the mode,
Mode = 3 hours [ANSWER]
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c)
Consider:
Thus,
E(x) = Expected value = mean = Sum(xP(x)) = 10.268 [ANSWER, MEAN]
Var(x) = E(x^2) - E(x)^2 = 28.732176
s(x) = sqrt [Var(x)] = 5.360240293 [ANSWER, STANDARD DEVIATION]
x P(x) 1 0.092 2 0.16 3 0.2 4 0.18 5 0.148 6 0.052 7 0.016 8 0.152Related Questions
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