Question

tossing coins find the mean, variance, and standard deviation for the number of heads when 20 coins are tossed. round your answers to three decimal places.
part: 0 / 2
part 1 of 2
(a) find the mean.
mean: \\( \mu = \square \\)

Explanation:

Step1: Identify binomial parameters

Number of trials $n=20$, probability of head $p=0.5$

Step2: Calculate mean using $\mu = np$

$\mu = 20 \times 0.5 = 10$

Step3: Calculate variance using $\sigma^2 = np(1-p)$

$\sigma^2 = 20 \times 0.5 \times 0.5 = 5$

Step4: Calculate standard deviation using $\sigma = \sqrt{\sigma^2}$

$\sigma = \sqrt{5} \approx 2.236$

Answer:

Mean: 10
Variance: 5
Standard deviation: 2.236