Question

Select the best alternative. Kim, a meteorologist at the local TV station, looks at the rain predictions from the National Weather Service for her service area. These are the numbers: Amount (inches) Probability (percent) 0.0 30 0.5 20 1.0 15 2.0 10 3.0 5 4.0 5 6.0 10 8.0 5 What total will Kim predict? She will predict 2.00 inches. She will predict a little bit less than two inches. She will predict zero inches. She does not have enough information to make any prediction.

Answer 1

Here, we will find E(x) or mean that will give true representation of prediction based on probabilities.

E(X) = $\sum$ 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

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