Question

Based on historical data, your manager believes that 43% of the company's orders come from first-time customers. A random sample of 243 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.2 and 0.39?

Answer 1

Following are the solution to the question:

Explanation:

`p = 0.43\\\\n = 243\\\\\sigma =\sqrt{(p(1-p))/(n)}=\sqrt{(0.43 (1 -0.43))/(243)}=0.0013`

z-score for
`\hat{p}=0.2` will be:

z score for will be:

`z=\frac{\hat{p}-p}{\sigma}=(0.39 - 0.43)/(0.0013)=-30.76`

`P(0.2 <\hat{p}< 0.39) = P(-176.92 < z < -30.76)` using excel method to calculate the value.