Question

The monthly demand for a product is normally distributed with mean = 700 and standard deviation = 200.

Answer 1

Answer:  a)  0.1587  b)  0.0618

Step-by-step explanation:

Let x be the random variable that  represents the monthly demand for a product.

Given : The monthly demand for a product is normally distributed with mean = 700 and standard deviation = 200.

i.e. $\mu=700$   and  $\sigma=200$

a) Using formula $z=\dfrac{x-\mu}{\sigma}$, the z-value corresponds to x= 900 will be :

$z=\dfrac{900-700}{200}=1$

Now, by using the standard normal z-table , the probability demand will exceed 900 units in a month :-

$P(z>1)=1-P(z\leq1)=1-0.8413=0.1587$

Hence, the probability demand will exceed 900 units in a month=0.1587

a) Using formula $z=\dfrac{x-\mu}{\sigma}$, the z-value corresponds to x=  392 will be :

$z=\dfrac{ 392-700}{200}=-1.54$

Now, by using the standard normal z-table , the probability demand will be less than 392 units in a month :-

$P(z$

Hence, the probability demand will be less than 392 units in a month = 0.0618