Question

If x is a binomial random variable with n=10 and p=0.8, the standard deviation of x is _________?

1) 8.0
2) 1.26
3) 1.60
4) 64.0
5) 10

Answer 1

The standard deviation of the binomial random variable x with n=10 and p=0.8 is calculated as 1.26 using the formula for standard deviation σ = √(npq).

Step-by-step explanation:

If x is a binomial random variable with n=10 and p=0.8, the standard deviation of x is calculated using the formula σ = √(npq), where p is the probability of success on any given trial, q is the probability of failure (q=1-p), and n is the total number of trials.

First, we calculate q as q = 1 - p = 1 - 0.8 = 0.2. Then, plugging in the values into the formula for the standard deviation, we get: σ = √(10 × 0.8 × 0.2) = √(1.6) = 1.26.

Therefore, the standard deviation of the binomial random variable x is 1.26.