Suppose the average number of donuts a nine-year old child eats in a month between 0.5...

Suppose the average number of donuts a nine-year old child eats in a month between 0.5 and 5 minutes, inclusive. Let X the average number of donuts a nineyear old child eats in a month. (Round probabilities to 4 decimal places) a. Then X ~ f(x) =

b. Find the probability that a randomly selected nine-year old child eats on average more than 2 donuts in month.

c. Find the 90th percentile for the average number of donuts a nine-year old child eats per month.

d. Find the probability that a different nine-year old child eats an average of more than two donuts given that his or her average is more than 1 donut per month.

Solutions

Expert Solution

(a)

Here X has uniform distribution between 0.5 and 5.

The pdf of X is

(b)

The probability that a randomly selected nine-year old child eats on average more than 2 donuts in month is

(c)

The 90th percentile, let P, for the average number of donuts a nine-year old child eats per month is,

(d)

and

Therefore,

The probability that a different nine-year old child eats an average of more than two donuts given that his or her average is more than 1 donut per month is,

orchestra answered 1 year ago

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