A humane society reports that 19% of all pet dogs were adopted from an animal shelter. Assuming the truth of this assertion, find the probability that in a random sample of80 per dogs, between 15% and 20% were adopted from a shelter. You may assume thatthe normal distribution applies.

The probability of pet dogs adopted between 15% and 20% is 0.4096.

Explanation:

Let X = number of pet dogs adopted from an animal shelter.

The proportion of pet dogs adopted from an animal shelter is, p = 0.19.

The sample of pet dogs selected is of size, n = 80.

A Normal approximation to Binomial can be applied in this case since,

So the sample proportion () of pet dogs adopted from an animal shelter follows a normal distribution.

Mean of is:

Standard deviation of is:

Compute the probability of between 15% and 20% as follows:

Thus, the probability of pet dogs adopted between 15% and 20% is 0.4096.

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