Given the following discrete probability distribution, XP(x) 42 0.375 65 0.15 70 0.225 75 0.05 90 0.2 (а). (b). Calculate the variance of x. (c) Calculate the standard deviation of x Calculate the expected (average) value of x.

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Given the following discrete probability distribution,
|x P(x)
| 42 0.375
65 0.15
70 0.225
75
0.05
90
0.2
(a). Calculate the expected (average) value of x.
(b). Calculate the variance of x.
(c) Calculate the standard deviation of x
QUESTION 5
A government agency wants to test a refining company's
claim that the mileage achieved with its unleaded gasoline
(A) is at equal or less than that achieved with its leaded
gasoline (B). Fifteen car models are chosen; a given
driver drives each model twice over the identical route. At
random, each driver is given brand A or brand B first,
then drives with the other brand during the second trip.
This procedure is designed to conduct a sign test at the 2.5
percent level of significance is chosen. Make the test,
using the government's following Table data.
TABLE: Gasoline Experiment
Miles per Gallon
Car Model Unleaded Gas (A) Leaded Gas (B)
22.1
23.7
2
15.7
16.1
3
18.2
19.0
4
19.0
19.0
5
25.7
24.2
6.
19.2
22.0
7
11.9
12.1
8
28.0
30.2
9.
35.0
37.8
10
27.0
30.0
11
19.7
19.0
12
16.3
15,1
13
21.2
23.4
14
22.2
20.7
15
27.8
28.1
Transcribed Image Text:Given the following discrete probability distribution, |x P(x) | 42 0.375 65 0.15 70 0.225 75 0.05 90 0.2 (a). Calculate the expected (average) value of x. (b). Calculate the variance of x. (c) Calculate the standard deviation of x QUESTION 5 A government agency wants to test a refining company's claim that the mileage achieved with its unleaded gasoline (A) is at equal or less than that achieved with its leaded gasoline (B). Fifteen car models are chosen; a given driver drives each model twice over the identical route. At random, each driver is given brand A or brand B first, then drives with the other brand during the second trip. This procedure is designed to conduct a sign test at the 2.5 percent level of significance is chosen. Make the test, using the government's following Table data. TABLE: Gasoline Experiment Miles per Gallon Car Model Unleaded Gas (A) Leaded Gas (B) 22.1 23.7 2 15.7 16.1 3 18.2 19.0 4 19.0 19.0 5 25.7 24.2 6. 19.2 22.0 7 11.9 12.1 8 28.0 30.2 9. 35.0 37.8 10 27.0 30.0 11 19.7 19.0 12 16.3 15,1 13 21.2 23.4 14 22.2 20.7 15 27.8 28.1
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