Question

A girl scout and her mom are setting up a table to sell cookies in front of a grocery store. They have available 3 boxes of Samoas, 4 boxes of Tagalons, 6 boxes of Do-si-dos, and 7 boxes of Trefoils. Each box sells for $5.

a.) Define random variable you will need.

b.) Determine the probability distribution and parameters for the random variable defined.

c.) Suppose that, after two hours, ten boxes of cookies have been purchased. Determine the cumulative distribution function for the number of Samoas purchased.

d.) Draw the probability distribution function for the number of Samoas purchased.

Answer 1

a.

random variable X : type of cupcake they sell

it can be : { samoas , tagalons, do-si-dos, trefoils }

b.

parameter :

total boxes = 3+4+6+7 = 20

distribution :

P(X) = no. of boxes of X / total boxes

P(samoas) = 3/20

P(tagalons) = 4/20

P(do-si-dos) = 6/20

P(trefoils) = 7/20

c.

x = no. of samoas purchased out of 10

x can be : 0,1,2,3

no. of samoas boxes = 3

no. of non samoas boxes = 20-3 = 17

P(x samoas purchased out of 10) = (select x samoas out of 3)*(select (10-x) non samoas out of 17) / (select 10 boxes from 20 boxes)

= 3Cx * 17C(10-x) / (20C10)

= 3Cx * 17C(10-x) / 184756 {x={0,1,2,3}}

cummulative probability distribution = P(x<=X) = P(0) + P(1) + ...+P(X) {x={0,1,2,3}}

d.

probability distribution function for the number of samoas purchased :

P(x samoas purchased out of 10) = (select x samoas out of 3)*(select (10-x) non samoas out of 17) / (select 10 boxes from 20 boxes)

= 3Cx * 17C(10-x) / (20C10) {x={0,1,2,3}}

= 3Cx * 17C(10-x) / 184756 {x={0,1,2,3}}

(please UPVOTE)