Question

the austrainian sheep dog is a breed renowned for its intelligence and work ethic.it is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. a sample of 15 adult dogs is studied.what is the standard deviation of the number of dogs who weigh 65 ils or more

Answer 1

The standard deviation of the number of dogs who weigh 65 pounds or more is 1.93.

Explanation:

For each dogs, there are only two possible outcomes. Either they weigh less than 65 pounds, or they weight at least 65 pounds. The probability of a dog weighing more than 65 pounds is independent of other dogs. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

`√(V(X)) = √(np(1-p))`

It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more.

This means that
`p = 0.45`

Sample of 15 adult dogs is studied.

This means that
`n = 15`

What is the standard deviation of the number of dogs who weigh 65 pounds or more

`√(V(X)) = √(np(1-p))[ = √(15*0.45*0.55) = 1.93`

The standard deviation of the number of dogs who weigh 65 pounds or more is 1.93.