Question
In: Statistics and Probability
According to a Gallup Poll, 18% of Americans surveyed said that they had gained “a lot”...
According to a Gallup Poll, 18% of Americans surveyed said that they had gained “a lot” of weight in the past five years. Assume that this result is true for the current population of Americans. A random sample of 14 Americans is selected.
a.Find the probability that in a random sample of 14 Americans, the number who will say they have gained “a lot” of weight in the past five years is at most 2. Draw a distribution
b. Find the probability that in a random sample of 14 Americans, the number who will say they have gained “a lot” ofweights in the past five year is greater than3. Draw a distribution
Solutions
Expert Solution
a)
The following information has been provided about the population proportions and the sample size:
| Population Proportion = | 0.18 |
| Sample Size = | 14 |
2/14 = 0.1428
We need to compute 
. Based on the information provided, the population men of sample
proportions and the corresponding standard error are:
Now, the following is obtained using normal approximation:
The following information has been provided about the population proportions and the sample size:
| Population Proportion = | 0.18 |
| Sample Size = | 14 |
3/14 = 0.2143
We need to compute 
. Based on the information provided, the population men of sample
proportions and the corresponding standard error are:
Now, the following is obtained using normal approximation:
orchestra answered 2 years agoRelated Solutions
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Binomial
n
25
p
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xi
P(X<=xi)
0
0.0000
1
0.0000
2
0.0001
3
0.0007
4
0.0031
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0.0112
6
0.0323
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0.0773
8
0.1569
9
0.2750
10
0.4235
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0.5826
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0.7285
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0.8431
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0.9203
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0.9647
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0.9866
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