In testing a new drug, researchers found that 20% of all patients using it would have a mild side effect. A random sample of 25 patients using the drug is selected. Find the mean and standard deviation of patients having a mild side effect.

Mean = np = 25(.2) = 5

Standard deviation = sqrt((25 * .2*.8))
= 2

To find the mean and standard deviation of patients having a mild side effect, we need to use the information given in the problem and apply some basic statistical formulas.

First, let's calculate the mean. The mean (μ) is found by multiplying the probability of having a side effect (p) by the number of trials (n):

μ = p * n

In this case, the probability of having a mild side effect is given as 20% or 0.2, and the number of trials is 25. Substituting these values into the formula, we can calculate the mean:

μ = 0.2 * 25
μ = 5

So, the mean number of patients having a mild side effect is 5.

Next, let's calculate the standard deviation. The standard deviation (σ) can be found using the formula:

σ = √(p * (1 - p) * n)

Using the same values of probability (p = 0.2) and number of trials (n = 25), we can substitute them into the formula and calculate the standard deviation:

σ = √(0.2 * (1 - 0.2) * 25)
σ = √(0.2 * 0.8 * 25)
σ = √(4)
σ = 2

So, the standard deviation of patients having a mild side effect is 2.

In summary, the mean number of patients having a mild side effect is 5, and the standard deviation is 2.