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**Normal Distribution Assignment**

**Question: Suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?**

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**Solution: **The Solution stated below needs to define the probability mean in to condition one when the Stock of the organisation is 180 and when the stock is out condition which is where the condition is less than 180.

The demand for the company is normally distributed as follows: -

Week |
1 |
2 |
3 |

Mean |
50 |
45 |
65 |

Standard Deviation |
10 |
5 |
15 |

It is essential to understand that the weekly demands are probabilistic in nature on the more they are the solutions can be derived with the sum of variances and sum od standards deviation

To understand the solution: -

The sum of means = Mean of Week 1 + Mean of Week 2 + Mean of Week 3 = 50 + 45 + 65 = 160

The sum of Variance = Variance of Week 1 + Variance of Week 2 + Variance ofWeek 3

= (10) 2 + (5) 2 + (15) 2 = 100 + 25 + 225 = 350

Thus, the standard deviation of three weeks of demand = Square Root 350 = 18.71

Hence, for a given distribution X = 160, SD = 18.71

For the probability = P (X> 180)

Applying the formula of Normal DISTRIBUTION = NORMDIST (Probability, Mean, STDEV)

In case if the stock comes to 180 then the probability= NORMDIST (180, 160, 18.71) = 0.8575 = 85.75 Percent

In case if the stock runs out of stock then the probability = 1 - 0.8575 = 0. 1425 = 14.25 Percent

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