Question

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 141 eligible voters aged​ 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged​ 18-24, 22% of them voted. Probability that fewer than 36 voted

Answer 1

Answer: 0.8770

Step-by-step explanation:

Given : The number of eligible voters aged​ 18-24 are randomly selected : n=141

The population proportion of eligible voters aged​ 18-24 : p=0.22

Then, mean : $np=141(0.22)=31.02$

Standard deviation: $\sqrt{np(1-p)}=\sqrt{141(0.22)(1-0.22)}\approx4.92$

We assume that this is normal distribution.

Let X be a binomial variable.

For x =36

$z=\dfrac{x-\mu}{\sigma}\\\\ z=\dfrac{36-31.02}{4.29}\approx1.16$

The probability that fewer than 36 voted will be :-

$P(x$