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 four 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:

0.369 is the probability that the buyer will not place an order.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 220 HP

Standard Deviation, σ = 15 HP

We assume that the distribution of average power is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(sample mean is less than 215 HP)

$P( x < 215) = P( z < \displaystyle\frac{215 - 220}{15}) = P(z < -0.3334)$

Calculation the value from standard normal z table, we have,  

$P(x < 215) =0.369= 36.9\%$

0.369 is the probability that the buyer will not place an order.