Homework SourseQuestion 1 Use the following information for question 13 Let
Question 1
Use the following information for question #1-3.
Let X = the number of days per week that a client uses a particular exercise facility. The table represents data from a random sample of 100 clients.
X
Frequency
0
3
1
12
2
33
3
28
4
11
5
9
6
4
What value represents the 80th percentile?
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A. 3
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B. 4
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C. 5
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D. 6
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E. 80
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What is the mean number of days per week a client uses this particular exercise facility?
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A. 2
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B. 2.75
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C. 3
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D. 3.5
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E. 14.286
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What value is 1.5 standard deviations below the mean?
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A. 0.701
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B. 1.384
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C. 2
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D. 4.116
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E. -3.301
Use the following information for question #1-3. Let X = the number of days per week that a client uses a particular exercise facility. The table represents data from a random sample of 100 clients.
What value represents the 80th percentile?
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| What is the mean number of days per week a client uses this particular exercise facility?
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| What value is 1.5 standard deviations below the mean?
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Solution
1)
There are 100 data points here. Thus, for the 80th percentile, 80 data points is lower than it.
Thus, it is the 81st lowest entry. Adding up the frequencies, we see that the 80th entry is at at x = 4. [ANSWER, B]
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2.
Consider the table:
Thus,
Mean = Sum(f*x) / Sum(f) =275/100 = 2.75 [ANSWER, B]
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3.
As
s = sqrt {[sum(x^2) - sum(x)^2/n]/(n-1),}
s = sqrt {(941 -275^2/100)/(100-1)} = 1.3661
Thus,
u - 1.5s = 2.75 - 1.5*1.3661 = 0.701 [OPTION A]
| x | f | f*x |
| 0 | 3 | 0 |
| 1 | 12 | 12 |
| 2 | 33 | 66 |
| 3 | 28 | 84 |
| 4 | 11 | 44 |
| 5 | 9 | 45 |
| 6 | 4 | 24 |
| Total | 100 | 275 |
