Answer:
The standard deviation of the number of dogs who weigh 65 pounds or more is 1.93.
Step-by-step 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:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more.
This means that [tex]p = 0.45[/tex]
Sample of 15 adult dogs is studied.
This means that [tex]n = 15[/tex]
What is the standard deviation of the number of dogs who weigh 65 pounds or more
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[ = \sqrt{15*0.45*0.55} = 1.93[/tex]
The standard deviation of the number of dogs who weigh 65 pounds or more is 1.93.
