Question

Norb and Gary are entered in a local golf tournament. Both have played the local course many times. Their scores are random variables with the following means and standard deviations.

Norb, x₁: μ₁ = 135; σ₁ = 12
Gary, x₂: μ₂ = 120; σ₂ = 18

In the tournament, Norb and Gary are not playing together, and we will assume their scores vary independently of each other.

(a) The difference between their scores is

W = x₁ − x₂.

Compute the mean, variance, and standard deviation for the random variable W. (Round your answers to one decimal place.)

μ
σ2
σ

(b) The average of their scores is

W = 0.5x₁ + 0.5x₂.

Compute the mean, variance, and standard deviation for the random variable W. (Round your answers to one decimal place.)

μ
σ2
σ

(c) The tournament rules have a special handicap system for each player. For Norb, the handicap formula is

L = 0.8x₁ − 3.

Compute the mean, variance, and standard deviation for the random variable L. (Use 2 decimal places.)

μ
σ2
σ

(d) For Gary, the handicap formula is

L = 0.95x₂ − 9.

Compute the mean, variance, and standard deviation for the random variable L. (Use 2 decimal places.)

μ
σ2
σ

Answer 1

a)

E(W) =μ=E(x1)-E(x2)=15
Var(W) =σ2=(1)^2*Var(x1)+(-1)^2*Var(x2)=468
SD(W)=σ=√Var(W)=21.63

b)

E(W) =μ=0.5E(x1)+0.5E(x2)=127.5
Var(W) =σ2=(0.5)^2*Var(x1)+(0.5)^2*Var(x2)=117
SD(W)=σ=√Var(W)=10.82

c)

μ =0.8*135-3 =105

σ2 =0.8^2*144=92.16

σ =sqrt(92.16)=9.6

d)

μ =0.95*120-9=105

σ2 =0.95^2*324 =292.41

σ=sqrt(292.41)=17.1