Here, we will find E(x) or mean that will give true representation of prediction based on probabilities.
E(X) =
X*P(X)
amount(in inches) | Probability | Probability | X*P(x) |
0 | 30 | 0.3 | 0 |
0.5 | 20 | 0.2 | 0.1 |
1 | 15 | 0.15 | 0.15 |
2 | 10 | 0.1 | 0.2 |
3 | 5 | 0.05 | 0.15 |
4 | 5 | 0.05 | 0.2 |
6 | 10 | 0.1 | 0.6 |
8 | 5 | 0.05 | 0.4 |
Total | 100 | 1 | 1.8 |
Kim will predict 1.8 inches i.e.,
Kim will predict little less than two inches.
2. Sample:
63 |
18 |
45 |
25 |
25 |
19 |
32 |
26 |
18 |
18 |
33 |
31 |
14 |
14 |
20 |
34 |
51 |
18 |
18 |
28 |
Weekly gas expenditure =
27.5 |
Standard deviation of weekly gas expenditure =
12.9432 |
1 standard deviation limits = 27.5 -/+12.9432 =
14.5568 | 40.4432 |
No. of observation between these limits are: 15
2 standard deviation limits = 27.5 -/+2*12.9432 =
1.613609 | 53.38639 |
No. of observation between these limits are: 19
Probability = 19/20 = 0.95
Please rate my answer and comment for doubt
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