Question

The standard deviation of a binomial distribution with n = 15 and p = 0.3 is:

• A. 2.48
• B. 3.00
• C. 2.64
• D. 1.77

Answer 1

Answer: (D)

1.77

Answer 2

The standard deviation ($\sigma$) of a binomial distribution is given by the formula:

$\sigma = \sqrt{np(1-p)}$

Given:

• Number of trials, $n = 15$
• Probability of success, $p = 0.3$

First, calculate the probability of failure, $q$: $q = 1 - p = 1 - 0.3 = 0.7$

Now, substitute the values of $n$, $p$, and $q$ into the formula for standard deviation: $\sigma = \sqrt{15 \times 0.3 \times 0.7}$ $\sigma = \sqrt{4.5 \times 0.7}$ $\sigma = \sqrt{3.15}$

Calculate the square root of 3.15: $\sigma \approx 1.7748$

Rounding to two decimal places, $\sigma \approx 1.77$.