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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?

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Answer:

43 ; 0.88493

Step-by-step explanation:

Using the Zscore formula :

Zscore = (x - m) / s

m = mean ; s = standard deviation

Profit = $1.5 - $1.2 = $0.3

Loss = $1.2 - $1 = 0.2

Cummlative probability :

Profit / (profit + loss)

0.3 / (0.3 + 0.2) = 0.3 / 0.5 = 0.6

To obtain the x, at Z at 0.6 = 0.26

m = 40 ; s= 10

Hence,

0.26 = (x - 40) / 10

0.26 * 10 = x - 40

2.6 = x - 40

2.6 + 40 = x

x = 42.6 `; 43 approximately

Probability of meeting day's demand at Wrigley

x = 52

P(x < 52) :

Zscore = (52 - 40) / 10

P(Z < 1.2)

Z = 0.88493

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