Question

In a study, 42% of adults questions reported that their health was excellent. A researcher wishes to study the health of people living close to a coal power plant. Among the 14 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 14 adults are randomly selected from the full population, only 3 or fewer report having excellent health.

Answer 1

Answer: 0.0594

Step-by-step explanation:

Given : The population proportion of adults questions reported that their health was excellent : p = 0.42

Among the 14 adults randomly selected from this area, only 3 reported that their health was excellent.

i.e. Sample size : n= 14

$\mu=np = 14\times0.42=5.88$

$s=\sqrt{np(1-p)}=\sqrt{14(0.42)(1-0.42)}\approx1.85$

z-score : $z=\dfrac{{x}-\mu}{\sigma}$

Put x= 3

$z=\dfrac{3-5.88}{1.85}\approx-1.56$

Then, the probability that only 3 or fewer report having excellent health:-

$P(z\leq-1.56)=0.0593799\approx0.0594$

Hence, the required probability : 0.0594