a) P(at least 16 years old) = P(16 years old) + P(17 years old) + P(18 years old) + P(19 years old) P(at least 16 years old) = 0.211+0.321+0.151+0.084 = 0.767

There is a 0.767 probability that if a student athlete is at least 16 years old if chosen from the district at random.

b) E(x) = mux = âxi * Pi = (14*0.094)+(15*0.139)+(16*0.211)+(17*0.321)+(18*0.151)+(19*0.084) = 16.548 years

The expected age of a randomly-selected student-athlete is 16.548 years.

c) Binomial Distribution Conditions:

**Binary** - at least 16 or under 16, **Independent** - since you can only be in no more than one age group, the student-athletesâ ages are independent, **Number of Trials** = there are five students who are selected (n=5), **Same Probability** = probability of being at least 16 is the same for each student-athlete (p = 0.767)

X = the number of student-athletes that are at least sixteen years old where the distribution of x is binomial with p = 0.767 and n = 5

Using binomial cdf on TI Calculator with n = 5, p = 0.767, lower bound = 4, upper bound = 5, the calculated probability is 0.6686.

There is a 0.6686 probability that 4 or 5 of the selected athletes are at least 16 years old if a random sample of 5 student-athletes is selected.