A hot dog vendor at Wrigley Field sells hot dogs for $1.50 each. He buys them fo

Question

A hot dog vendor at Wrigley Field sells hot dogs for
$1.50 each. He buys them for $1.20 each. All the hot dogs
he fails to sell at Wrigley Field during the afternoon can be
sold that evening at Comiskey Park for $1 each. The daily
demand for hot dogs at Wrigley Field is normally distributed
with a mean of 40 and a standard deviation of 10.

a) If the vendor buys hot dogs once a day, how many
    should he buy?
b) If he buys 52 hot dogs, what is the probability that he
   will meet all of the day’s demand for hot dogs at Wrigley?

Explanation / Answer

mean of 40 and a standard deviation of 10.

ok you should know this farmula

he should by such that probability of loss equal to probability of profit

cumulative probality =(profit)/(profit + Loss)

profit =1.5 -1.2 =0.3

loss =1.2 -1 =0.2

so CP =0.6 hence z=0.26

so

he should buy items equal

= + z =40 +0.26*10 =42.6 ~ 43

b) so the demand should be less than 52

using normal table z =(52 - 40)/10

z=1.2

hence P =0.8849

hence 88.49% of the time demand will be met

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