Question

There is a sample of 500 and the population proportion is 0.47. What is the probability that the proportion is greater then 0.50

Answer 1

Answer: 0.0895

Explanation:

Let p= population proportion.

Given : Sample size : n= 500

p= 0.47

Required probability =
`P(\ha{p}>0.50)`

`=P(\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}>\frac{0.50-0.47}{\sqrt{(0.47(1-0.47))/(500)}}) \\\\=P(z>1.344)\ \ \ [z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}]\\\\=1-P(z<1.344)\\\\=1-0.9105\approx0.0895`

Hence, required probability = 0.0895