3. The retail price of a box of a Captain Crisp cereal ranges from $2.80 to S3.1

Question

3. The retail price of a box of a Captain Crisp cereal ranges from $2.80 to S3.14. Assume the prices are uniformly distributed. You interested in likelihood of prices of the cereal. a) (lpt) Define a random variable for this problem. b) (2pts) What are the average price and the standard deviation of prices in this distribution? Interpret these values. c) (1.5pts) If a price is randomly selected what is the probability that it will be between $3.00 and $3.10? d) (.5pts) If a price is randomly selected what is the probability that it will be under S3? range of prices would be considered the "sale pri ces"?

Explanation / Answer

a) Let X be the price of cereal randomly selected.

X ~ U (2.8 , 3.14)

b) Average = (3.14 + 2.8) / 2 = 2.97

standard deviation = (3.14 - 2.8) / sqrt(12) = 0.1

c) P(3 < X < 3.1) = (3.1 - 3) / (3.14 - 2.8) = 0.29

d) P(X < 3) = (3 - 2.8) / (3.14 - 2.8) = 0.59

e) P(X < x) = 0.3

or, (x - 2.8) / (3.14 - 2.8) = 0.3

or, x - 2.8 = 0.3 * 0.34

or, x = 2.902

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