Question

he director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience.

Admissions	Probability
1,200	.2
1,300	.3
1,000	.5

Answer 1

Given data,

Admissions	Probability
1,200	.2
1,300	.3
1,000	.5

From the given information let X be the number of admissions for the fall semester.

expected number of admissions = Mean = E(X) = Σ x P(X=x)

= Σ x P(X=x)

=(1200 * 0.2) + (1300 * 0.3) + (1000 * 0.5)

=240 + 390 + 500

=1130

Therefore, E(X) = 1130

Variance of the number of admissions= Var (X) = E(X²) - [E(X)]²

E(X²) = Σ X² P(X=x) = (1200² *0.2) + (1300² *0.3) + (1000² * 0.5) = 288000 + 507000 + 500000 =1295000

Therefore

Var (X) = E(X²) - [E(X)]² = 1295000 - 1130²  =1295000-1276900 = 18100

Standard deviation of the number of admissions = √ Var(X) =√ 18100 = 134.5362.