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 : [tex]\mu=2.5\text{ million}=2.5\times1000000=2500000[/tex]
Standard deviation : [tex]\sigma=300000[/tex]
To find : Probability that the firm’s sales will exceed $3 million i.e. $ 3,000,000.
∵ [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Then , for x= 3,000,000
[tex]z=\dfrac{3000000-2500000}{300000}=1.67[/tex]
Then , the probability that the firm’s sales will exceed $3 million is given by :-
[tex]P(z>1.67)=1-P(z<1.67)\\\\=1-0.9525403=0.0474597\approx0.0475[/tex]
Hence, the probability that the firm’s sales will exceed $3 million = 0.0475
