The average demand for rental skis on winter Saturdays at a

The average demand for rental skis on winter Saturdays at a particular area is 150 pairs, which has been quite stable over time. There is variation due to weather conditions and competing areas; the standard deviation is 20 pairs. The demand distribution seems to be roughly normal.

A) The rental shop stocks 170 pairs of skis. What is the probability that demand will exceed this supply on any winter Saturday?

B) How many pairs of skis in stock does the shop have to have to make the probability in question (a) less than .01?

Solution

Normal Distribution
Mean ( u ) =150
Standard Deviation ( sd )=20
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 170) = (170-150)/20
= 20/20 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587                  
b)
P ( Z < x ) = 0.01
Value of z to the cumulative probability of 0.01 from normal table is 2.326
P( x-u/s.d < x - 150/20 ) = 0.01
That is, ( x - 150/20 ) = -2.33
--> x = 2.33 * 20 + 150 = 196.4