Question

A new drug has been found to be effective in treating 75% of the people afflicted by a certain disease. If the drug is administered to 400 people who have this disease, what are the mean and the standard deviation of the number of people for whom the drug can be expected to be effective? (Round your standard deviation to two decimal places.)

Answer 1

This can be solved by using the normal approximation to the binomial distribution. Let n be the number of people who have the disease and have the drug administered. Let p be the probability that the drug is effective. Then the mean number of people for whom the drug is effective is given by:

np = 400×0.75 = you can calculateThe standard deviation is given by:
√(np(1-p)) = √(400 x 0.75 x 0.25)
I believe you can calculate it now,
I hope my answer helped you.

Answer 2

The mean is 300 and the standard deviation is 8.67.

Explanation:

It has been given that the drug has been found to be effective in treating 75% of the people afflicted by a certain disease.

Therefore, probability of success is given by p = 0.75

Now, total number of people affecting from the disease, n = 400

We know the formula for mean, which is given by

`\mu=np\\\mu=400* 0.75\\\mu=300`

And the standard deviation is

`\sigma=√(np(1-p))\\\sigma=√(400\cdot0.75(1-0.75))\\\sigma=8.67`

Therefore, the mean is 300 and the standard deviation is 8.67.