Question

1. The admission fee to a summer fair is $1 for children and seniors, and $3 for adults. Based on previous years, 65% of all visitors to the fair are adults. If 40 entrance tickets to the fair are purchased during a particular period, let X be the corresponding number of children and seniors.

(a) What is the distribution of X?

(b) What is the expected total ticket revenue during the period?

(c) What is the variance of the total ticket revenue during the period?

Answer 1

a) let X be the corresponding number of children and seniors

65% of all visitors to the fair are adults.

so, 35% of all visitors to the fair are children and seniors

b)

X	P(X)	X*P(X)	X² * P(X)
1	0.35	0.3500	0.3500
3	0.65	1.9500	5.8500

	P(X)	X*P(X)	X² * P(X)
total sum =	1	2.3	6.20

mean = E[X] = Σx*P(X) =            2.3000
expected total ticket revenue during the period = 40*2.3 = $92

c)

variance = E[ X² ] - (E[ X ])² =            0.9100
variance of the total ticket revenue during the period = 40^2*0.91 = 1456 dollars square