The explanation for the answer to the given question is as follows: Hence, the current stock available is 180 units. To find out the probability of the company running out of the stock of 180 units within a time of next 3 weeks, let’s take ' z ' as a value that should be checked in the standard deviation table in order to find the probability...
Let us first find the value of ' z ', for which we should know the mean demand of the period of 3 weeks: So to do this we can assume that the demand for week one is 65 units, for week two is 50 units and for week three is 45 units. Mean Demand of the period of 3 weeks is equal to the Sum of mean demands of per week that is,60+55+45 = 160
Now, let us determine the standard deviation for the period of 3 weeks, as it is mentioned in question. So, lets instead find variance of per week, and take
*…show more content…*

Hence, First week difference = 60 - 55 = 5. Second week difference = 55 - 45 = 10. Third week difference = 45 - 60 = -15. Variance for week one is 25. Variance for week two is 100.Variance for week three is 225. (Since square of any negative number gives us a positive number). Hence, variance of 3 weeks is equal to the Sum variance of per week that is, 25+100+225=350 Standard Deviation of 3 weeks is equal to the Square root of the variance of 3 weeks that is, Square root of 350 = 18.71. Now that we have the found the mean and standard deviation of 3 weeks, let’s find ' z ' value by using the formula:-Z = ( total value - total mean ) / standard deviation that is,Z = 180-160/18.71 = 1.07. Now we have to check the value of 1.07 in the standard deviation table, On checking we get the value as 85.77% this is probability that the units will be sufficient for the period of next 3 weeks, Hence, the probability of the company running out of units = 100 - 85.77. Therefore, the probability of the company running out of units is

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