The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 4 0% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 1 4 adult dogs is studied. What is the standard deviation of the number of dogs who weigh 65 lb or more?

The standard deviation of the number of dogs who weigh 65 lbs or more is 1.83.

Step-by-step explanation:

Let X represent the number of adult Australian sheep dogs weighing 65 pounds or more.

It is provided that the probability of occurrence of X is, p = 0.40.

A sample of n = 14 adult dogs is studied.

Each dog's weight is independent of the others.

The random variable X follows a Binomial distribution.

The standard deviation of a Binomial distribution is:

Compute the standard deviation of the number of dogs who weigh 65 lbs or more as follows:

Thus, the standard deviation of the number of dogs who weigh 65 lbs or more is 1.83.

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