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22higlebosa
11.06.2021 •
Mathematics
The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.17 and a sample of 900 households will be selected from the population. Use z-table.
a. Calculate σ(p), the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals).
b. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion (to 4 decimals)?
c. What is the probability that the sample proportion will be within +/- 0.02 of the population proportion for a sample of 1,400 households (to 4 decimals)?
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Ответ:
The right answer is:
(a) 0.01252
(b) 0.8882
(c) 0.9544
Step-by-step explanation:
Given:
Population proportion,
P = 0.17
Sample size,
n = 900
(a)
The standard error of proportion will be:
⇒![SE_p=\sqrt{\frac{P(1-P)}{n} }](/tpl/images/1371/0268/2b772.png)
By putting the values, we get
(b)
We know that,
Now,
⇒![z=\frac{\hat{P}-P}{\sqrt{\frac{P(1-P)}{n} } }](/tpl/images/1371/0268/b8721.png)
By substituting the values, we get
⇒![P(I\hat{P}-PI](/tpl/images/1371/0268/1846c.png)
(c)
We know that,
Now,
⇒![z=\frac{\hat{P}-P}{\sqrt{\frac{P(1-P)}{n} } }](/tpl/images/1371/0268/b8721.png)
By substituting the values, we get
⇒![P(I \hat P-PI](/tpl/images/1371/0268/ac31d.png)
Ответ:
13^2 - 12^2 = 5
15^2 - 12^2 = 9
5+9 = 14
14 is the length of each side of the square
14^2 + 14^2 = 19.8
19.8 is the diagonal length of the inside if the square