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shifaxoxoxo
09.01.2021 •
Advanced Placement (AP)
An opinion poll asks an SRS of 1500 adults, "Do you happen to jog?" Suppose that the population proportion who jog (a parameter) is p = 0.15. To estimate p, we use the proportion p-hat in the sample who answer "Yes." Justify the use of a normal approximation and find the following probabilities.
a) P(p > 0.16)
b) P(0.14
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Ответ:
0.14007 ; 0.71986
Explanation:
Given that :
Justification :
Mean = np ≥ 10
(1 - np) ≥ 10
n = sample size ; p = 0.15
q 1 - 0.15 = 0.85
np = 1500 * 0.15 = 225 > 10
nq = 1500 * 0.85 = 1275 > 10
Hence, the Justification
P(p" > 0.16)
P(Z > (p" - p) /sqrt(p(q) /n))
P(Z > (0.16- 0.15) /sqrt(0.15(0.85) /1500))
P(Z > 0.01 / 0.0092195)
P(Z > 1.08) = 0.14007
P(0.14 < p < 0.16)
P(Z (0.14- 0.15) /sqrt(0.15(0.85) /1500)) < Z < (0.16 - 0.15) /sqrt(0.15(0.85) /1500))
P(Z <-0.01 / 0.0092195) - 0.01 / 0.0092195)
P(Z < 1.08) - P(Z < - 1.08)
Using the Z probability m calculator :
0.85993 - 0.14007
= 0.71986
= 0.72208
Ответ:
Hi!
Assuming the 9in is the radius, we would multiply it by 2, or add it to itself. We then get 18 in.
Hope this helps!