Question

PBS News Hour reported in 2014 that 39.4% of Americans between the ages of 25 and 64 have at least a two-year college degree.† Assume that 55 Americans between the ages of 25 and 64 are selected randomly.
(a) What is the expected number of people with at least a two-year college-degree?
(b)What are the variance and standard deviation for the number of people with at least a two-year college degree? (Round your answers to four decimal places.)

Answer 1

Answer:

Mean = 22

Variance = 13.1320

Standard Deviation = 3.6238

Step-by-step explanation:

From the question, we can deduce that

n = 55 (sample)

p = 39.4% (proportion of those within the given range)

Solving (a): Expected Value, E(x)

This is calculated using the following formula.

E(x) = np

Substitute values for n and p

E(x) = 55 * 39.4%

E(x) = 55 * 0.394

E(x) = 21.67

E(x) = 22 ---- Approximated

Hence, the expected number of people is 22

Solving (b): Variance (σ²) and Standard Deviation (σ)

σ² is calculated as thus:

σ² = np(1 - p)

σ² = 55 * 39.4% * (1 - 39.4%)

σ² = 55 * 0.394 * (1 - 0.394)

σ² = 55 * 0.394 * 0.606

σ² = 13.13202

σ² = 13.1320 ---- Approximated

σ is calculated as follows:

σ = √σ²

Substitute value for σ²

σ = √13.13

σ = 3.6238 ----- Approximated