People arrive at the Durham Farmer’s market at rate 15 per hour. 4/5’s are veget

Question

People arrive at the Durham Farmer’s market at rate 15 per hour. 4/5’s are vegetarians, and 1/5 are meat eaters. Vegetarians spend an average of $7 with a standard deviation of 3. Meat eaters spend an average of $15 with a standard deviation of 8.

(a) Compute the probability that in the first 20 minutes exactly three vegetarians and two meat eaters arrive. You do not have to simplify your answer.

(b)Find the mean and standard deviation of the amount of money spent during the four hours the market is open.

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Explanation / Answer

a)

Here, 15 people arrive within an hour and so 5 would arrive in 20 minutes. The poisson distribution for 3/5 vegeterians and 2/5 meat eaters would 0.018.

b)

Vegeterians=4*15*4/5*7=336

Meat eaters=4*15*1/5*15=180

Mean=336+180=516/60=8.6

S.D=3.227 (putting 48 7's and 12 15's in excel) and calculating the standard deviation

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