Monthly demand for Under Armour\'s new basketball shoe is distributed continuous

Question

Monthly demand for Under Armour's new basketball shoe is distributed continuously and normally with a mean of 11,000 pairs and a standard deviation of 1,000 pairs. Suppose Under Armour produces 12,000 pairs of the shoe this month. Determine the probability at least 1, 500 pairs of the shoe will be unsold at the end of the month. Determine the probability the company has a shortage of no more than 500 pairs of the shoe at the end of the month. Determine the probability the company will not have a shortage of pairs of the shoe at the end of the month If Kevin Plank, the founder and CEO of Under Armour, Inc., sets the acceptable probability of a shortage of pairs of the shoe at the end of next month at 0.05, how many pairs of the shoe should the company produce?

Explanation / Answer

a) for 1500 pairs to be left unsold 10500 shoes need to be sold

hence P(X<10500) =P(Z<(10500-11000)/1000) =P(Z<0.5)=0.3085

b) for shortage of 500 jobs at max , demand should be less then 12500

P(X<12500)=P(Z<(12500-11000)/1000) =P(Z<1.5) =0.9332

c)for 0 shortage demand should be less then 12000

hence P(X<12000) =P(Z<(12000-11000)/1000) =P(Z<1) =0.8413

d)for 0.05 acceptable probabilty of a shoratge of pair of shoes , at 95% Z =1.6449

hence pair of shoes company should produce =mean +z*std deviation =11000+1.6449*1000 =12645

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