Question

Sixty-five percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?

(A) 0, 1, 2, 3, 8
(B) 0, 1, 2, 7, 8
(C) 1, 2, 3
(D) 0, 1, 2, 3

Answer 1

(a) 0, 1, 2, 3, 8

Explanation:

According to the range rule of thumb, most values should lie within 2 standard deviations of the mean; it is unusual for a value to differ from the mean by more than 2 standard deviations.

The unusual outcomes are going to be the ones outside of the interval:

(μ - 2σ, μ + 2σ)

For a binomial distribution:

μ = np = 8(0.65) = 5.2

σ = √(npq)

q = 1 - p = 1 - 0.65 = 0.35

σ = √(8×0.65×0.35) = 1.3

In this case the unusual outcomes, according to the range rule of thumb, are the ones outside the interval (2.6, 7.8)

The closest answer is (a)