Question

A candy machine contains over 1,000 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.

Answer 1

Answer:

μX = 4.5 candies

σX = 1.8 candies

Step-by-step explanation:

Answer 2

Using the binomial distribution, we find that the mean of X is of 4.5, while the standard deviation is of 1.8.

For each candy, there are only two possible outcomes, either it is blue, or it is not. The probability of a candy being blue is independent of any other candy, hence the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.  

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

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

In this problem:

• 15 candies in a purchase, hence $n = 15$

• 30% are blue, hence $p = 0.3$

Hence:

$E(X) = np = 15(0.3) = 4.5$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15(0.3)(0.7)} = 1.8$

The mean of X is of 4.5, while the standard deviation is of 1.8.

A similar problem is given at https://brainly.com/question/24261244