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Alexus [3.1K]
3 years ago
7

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

Mathematics
1 answer:
murzikaleks [220]3 years ago
7 0

Answer:

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

To Find :

1. What is probability demand will exceed 900 units in a month?

2. What is probability demand will be less than 392 units in a month?

Solution:

\mu = 700 \\\sigma = 200

We are supposed to find probability demand will exceed 900 units in a month.

Formula : z=\frac{x-\mu}{\sigma}

We are supposed to find P(Z>900)

Substitute x = 900

z=\frac{900-700}{200}

z=1

Refer the z table.

P(Z<900)=0.8413

P(Z>900)=1-P{(Z<900)=1-0.8413=0.1587

So, the probability that demand will exceed 900 units in a month is 0.1587.

Now we are supposed to find probability demand will be less than 392 units in a month

We are supposed to find P(Z<392)

Substitute x = 392

z=\frac{392-700}{200}

z=-1.54

refer the z table

P(Z<900)=0.0618

So, probability that demand will be less than 392 units in a month is 0.0618.

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