Question

The standard deviation of a binomial distribution for which n = 100 and p = .35 is

Answer 1

Answer:

How does radiation heat up the atmosphere

Answer 2

Answer:

The standard deviation of the binomial distribution is 4.77.

Explanation:

Given, the number of trials, n = 100

Probability of success of each trial, p = 0.35

The standard deviation(σ) of a probability distribution is the measure of the variability of possible outcomes.

In a binomial experiment, the standard deviation of the probability distribution X is equal to the square root of the variance.

where variance is given by $\sigma^{2} =np(1-p)$

And hence the formula for the standard deviation is $\sigma=\sqrt{np(1-p)}$

where n is the number of trials and p is the probability of success of each trial.

Substituting the given values,

$\sigma=\sqrt{100\times 0.35(1- 0.35)}$

$=\sqrt{35\times0.65}$

$=\sqrt{22.75}$

$\approx 4.77$

Therefore, the standard deviation of the binomial distribution is 4.77.