Answer to Question #342465 in Statistics and Probability for Ari

Question #342465

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


1
Expert's answer
2022-05-23T23:35:37-0400

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


μ=0.14,\mu=0.14,

σ=p(1p)n=0.14(10.14)115=0.0323567\sigma=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.14(1-0.14)}{115}}=0.0323567

P(X<0.1375)=P(Z<0.13750.140.0323567)P(X<0.1375)=P(Z<\dfrac{0.1375-0.14}{0.0323567})

P(Z<0.07726)0.4692\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.


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