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

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:
`√(np(1-p))=√(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=(x-\mu)/(\sigma)\\\\ z=(36-31.02)/(4.29)\approx1.16`

The probability that fewer than 36 voted will be :-

`P(x<36)=P(z<1.16)=0.8769756\approx0.8770`