Question

Based on data from a statistical abstract, only about 20% of senior citizens (65 years old or older) get the flu each year. However, about 28% of the people under 65 years old get the flu each year. In the general population, there are 12% senior citizens (65 years old or older). (Round your answers to three decimal places.)

(a) What is the probability that a person selected at random from the general population is senior citizen who will get the flu this season?


(b) What is the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year?


(c) Repeat parts (a) and (b) for a community that has 93% senior citizens.

(a)
(b)

(d) Repeat parts (a) and (b) for a community that has 48% senior citizens.

(a)
(b)

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 = 115; σ₁ = 14
Gary, x₂: μ₂ = 100; σ₂ = 8

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 − 12.

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 = 0.85x₂ − 5.

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

μ
σ2
σ

Answer 1