Question

The engines made by Ford for speedboats had an average power of 220 horsepower (HP) and standard deviation of 15 HP. A potential buyer intends to take a sample of forty 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

Answer:

0.3707

Step-by-step explanation:

The engines made by Ford for speedboats had an average power of 220 horsepower (HP) and standard deviation of 15 HP.

$\mu = 220$

$\sigma = 15$

A potential buyer will not place an order if the sample mean is less than 215 HP.

We are supposed to find What is the probability that the buyer will not place an order?

P(x<215)

Formula : $Z= \frac{x-\mu}{\sigma}$

x= 215

$Z= \frac{215-220}{15}$

$Z=-0.333$

refer the z table for p value

p value = 0.3707

Hence the probability that the buyer will not place an order is 0.3707

Answer 2

There is a probability of 1.74% that the buyer will not place an order.

What is the z score?

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

z = (raw score - mean) / (standard deviation ÷ √sample size)

Given that mean = 220, standard deviation = 15, sample size = 40

For x < 215

z = (215 - 220)/(15 ÷ √40) = -2.11

P(z < -2.11) = 0.0174

There is a probability of 1.74% that the buyer will not place an order.

Find out more on z score at: https://brainly.com/question/25638875