Ten percent of Americans adults are left-handed. A statistics class has 50 students in attendance.
Find the standard deviation for the number of left-handed students in such classes of 50 students
To find the standard deviation for the number of left-handed students in a class of 50 students, we need to use the formula for the standard deviation of a binomial distribution, since left-handedness is a binary variable (either left-handed or not left-handed).
The formula for the standard deviation of a binomial distribution is:
Standard deviation (σ) = √(n * p * q),
where:
- n is the sample size (number of students in the class),
- p is the probability of success (percentage of left-handed adults, which is 10% in this case), and
- q is the probability of failure (100% - p).
In this problem, n = 50 and p = 10% = 0.1. Therefore, q = 1 - p = 1 - 0.1 = 0.9.
Now, we can substitute these values into the formula and calculate the standard deviation:
σ = √(50 * 0.1 * 0.9)
= √(4.5)
≈ 2.121
So, the standard deviation for the number of left-handed students in a class of 50 students is approximately 2.121.