Answer to Question #176385 in Economics for Farhan Ishraq Abir

Question

Anticipated consumer demand for a product next month can be represented by a normal random variable with mean 1200 units and standard deviation 100 units.

a. What is the probability that sales will be between 1100 and 1300 units.

b. The probability is 0.10 that sales will be more than how many units.

Answer 1

a.

$$z_1=\frac {1300-1200}{100}=1$$

$$\phi(1)=0.8413$$

$$z_2=\frac {1100-1200}{100}=-1$$

$$\phi (-1)=-0.8413$$

$$p(1100<x<1300)=\frac {1}{2}(\phi(1)-\phi(-1))=0.8413$$

b.

$$1-0.1=0.9$$

$$\phi(z)=0.9$$

$$z=1.3$$

$$\frac {n-1200}{100}=1.3$$

$$n=1330$$