Answer to Question #342465 in Statistics and Probability for Ari

Question

What is the probability that, for the sample of 115 customers, the proportion who wait longer than five days for their order to be delivered is less than 13.75%? Interpret your answer

Answer 1

It has been found that 14% of customers of an online retail store wait longer than five days for their order to be delivered. We assume normal distribution

$$\mu=0.14,$$

$$\sigma=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.14(1-0.14)}{115}}=0.0323567$$

$$P(X<0.1375)=P(Z<\dfrac{0.1375-0.14}{0.0323567})$$

$$\approx P(Z<-0.07726)\approx0.4692$$

The probability that the proportion who wait longer than five days for their order to be delivered is less than 13.75% is 0.4692.