mean and variance of a binominal random variable

A candy machine contains over 1000 pieces of candy $30 \%$ of which are blue. Customers get an SRS of 15 candies in a purchase. Let $X =$ the number of blue candies that a random customer gets in a purchase.

Find the mean and standard deviation of X.
You may round your answers to the nearest tenth.

$\mu x$ = ? candies

$\sigma x$ = ? candies

4.5, 1.8

Solution:

(1) $\begin{align*}\mu x & = n p, \sigma x = \sqrt{np (1-p)} \\n & = 15, p = 0.3 \\\mu x & = 15 * 0.3 \\\sigma x & = \sqrt{15 * 0.3 * 0.7}\end{align*}$

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