The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 40% 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) 14
B) 1.833
C) 3.36
D) 5.6

Question

Quizplus · Accepted Answer

The standard deviation for a binomial distribution, which this scenario represents (dogs either weigh 65 lb or more, or they don't), is calculated using the formula $\sigma = \sqrt{n \cdot p \cdot (1-p)}$, where $n$ is the sample size and $p$ is the probability of success (in this case, a dog weighing 65 lb or more). Given $n = 14$ and $p = 0.40$, the calculation is $\sigma = \sqrt{14 \cdot 0.40 \cdot (1-0.40)} = \sqrt{14 \cdot 0.40 \cdot 0.60} = \sqrt{3.36} = 1.833$.

The Australian Sheep Dog Is a Breed Renowned for Its