In testing a new drug, researchers found that 20% of all patients using it will have a mild side effect. A random sample of 25 patients using the is selected. Find the mean and standard deviation of patients having a mild side effect.
I know the mean is 25(0.2)= 5 but I’m not sure where to go from there
To find the standard deviation of patients having a mild side effect, you can use the formula for the standard deviation of a binomial distribution. In this case, the binomial distribution represents the probability of success (having a mild side effect) in each trial (each patient).
The formula for the standard deviation of a binomial distribution is:
σ = √(n * p * (1 - p))
where:
- σ is the standard deviation
- n is the sample size
- p is the probability of success in each trial
Given that the sample size is 25 (n = 25) and the probability of having a mild side effect is 20% (p = 0.2), you can substitute these values into the formula:
σ = √(25 * 0.2 * (1 - 0.2))
Calculating this expression gives you:
σ = √(25 * 0.2 * 0.8)
= √(4)
So, the standard deviation of patients having a mild side effect is 2.
Therefore, the mean is 5 and the standard deviation is 2.