Question

Problem 18: The engines made by Ford for speedboats are normally distributed with an average power of 220 horsepower (HP) and standard deviation of 15 HP. A potential buyer intends to take a sample of 4 engines and will not place an order if the sample mean is less than 215 HP. What is the probability that the buyer will not place an order?

Answer 1

µ = 220

sd = 15

n = 4

$P(\bar{X}<215)=P(\frac{\bar{X}-\mu}{\sigma/\sqrt{n}}<\frac{215-\mu}{\sigma/\sqrt{n}})$

                           

215- 220 P15/V4

                            = P(Z < 0.67)

                            = 0.7475 (ans)