The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 25% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 14 adult dogs is studied.
What is the standard deviation of the number of dogs who weigh 65 lb or more?
A) 3.5
B) 14
C) 1.6202
D) 2.625

Question

Quizplus · Accepted Answer

We know that p = 0.25 (proportion of adult Australian sheep dogs weighing 65 pounds or more)
We also know that n = 14 (sample size)
Using the formula for the standard deviation of a binomial distribution, we get:

σ = sqrt(np(1-p))
σ = sqrt(14*0.25*0.75)
σ = 1.6202

Therefore, the standard deviation of the number of dogs who weigh 65 lb or more is 1.6202. Option C is the correct answer.

The Australian Sheep Dog Is a Breed Renowned for Its