Question

Afirm’s marketing manager believes that total sales X can be modeled using a normal distribution with mean m ¼ $2.5 million and standard deviation s ¼ $300,000. What is the probability that the firm’s sales will exceed $3 million?

Answer 1

Answer: 0.0475

Step-by-step explanation:

Given :  A firm’s marketing manager believes that total sales X can be modeled using a normal distribution.

Where , Population mean : $\mu=2.5\text{ million}=2.5\times1000000=2500000$

Standard deviation : $\sigma=300000$

To find : Probability that the firm’s sales will exceed $3 million i.e. $ 3,000,000.

∵ $z=\dfrac{x-\mu}{\sigma}$

Then , for x= 3,000,000

$z=\dfrac{3000000-2500000}{300000}=1.67$

Then , the  probability that the firm’s sales will exceed $3 million is given by :-

$P(z>1.67)=1-P(z$

Hence, the probability that the firm’s sales will exceed $3 million = 0.0475