Question

Calculate the expected value, the variance, and the standard deviation of the given random variable X. (Round all answers to two decimal places.) Twenty darts are thrown at a dartboard. The probability of hitting a bull's-eye is .2. Let X be the number of bull's-eyes hit.
expected value
variance
standard deviation

Answer 1

Answer:

The answer is "4.8, 3.84, and 1.96".

Step-by-step explanation:

Given:

$\to p = 0.2\\\\\to q = 1 - p = 1 - 0.2 = 0.8\\\\\to n = 24$

By using the binomial distribution:

$\to Mean(\mu) = n \times p = 24 \times 0.2 = 4.8\\\\\to variance (\sigma^2) = n \times p \times q = 24 \times 0.2 \times 0.8 = 3.84\\\\\to Standard \ deviation (\sigma) = \sqrt{n \times p \times q} = \sqrt{24 \times 0.2 \times 0.8} = 1.96$