The weekly demand of a cell phone shop is following the normal distribution with average number of cell phones sold is 200 units and it has also been found that 90% of time the demand is lying less than 220 units.
a. Using this information find the standard deviation of the distribution.
b. Determine the lowest stock that the company should maintain so that the probability of shortage is not higher than 5%.
Answers
Given : The weekly demand of a cell phone shop is following the normal distribution with average number of cell phones sold is 200 units and it has also been found that 90% of time the demand is lying less than 220 units.
To find : standard deviation of the distribution.
lowest stock that the company should maintain so that the probability of shortage is not higher than 5%.
Solution:
Mean = 200
90% of time the demand is lying less than 220 units.
for 90 % z score = 1.282
Z score = ( value - Mean)/SD
=> 1.282 = ( 220 - 200)/SD
=> 1.282 = 20/SD
=> SD = 15.6
standard deviation of the distribution. = 15.6
Lowest stock that the company should maintain so that the probability of shortage is not higher than 5%.
=> 95 % of time demand should meet
Z score for 95 % = 1.645
1.645 = ( value - 200)/(15.6)
=> Value = 225.66
=> Value = 226
226 is the lowest stock that the company should maintain so that the probability of shortage is not higher than 5%.
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