Question

Ms. Smith puts a variety of wrapped

Answer 1

Using the binomial distribution, it is found that the number of students that would be expected to select a gold-wrapped candy  from the bag is given by:

• B. 5 students

The candies are chosen with replacement, which means that for each student, the probability of choosing a gold wrapped candy is independent of any other student, hence the binomial distribution is used.

What is the binomial distribution?

• The binomial distribution is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

$E(X) = np$

In this problem:

• There are 15 students, hence $n = 15$.

• Of a totlal of 5 + 1 + 2 + 4 = 12 candies, 4 are gold wrapped, hence $p = \frac{4}{12} = \frac{1}{3}$

Then, the expected value is:

$E(X) = np = 15\times \frac{1}{3} = 5$

Hence, option B is correct.

To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377