Question

Of the 12 mystery boxes on a Master Chef Junior contest, 4 are
completely vegan. Suppose only 10 contestants have opened their
randomly assigned mystery boxes, and let X be the number of vegan
boxes that have been opened. Find the expected value of
X and its standard deviation

Answer #1

We can consider this as a binomial experiment where in the 12 boxes is the population and 10 opened are the samples. Here our successs event will be the boxes being vegan. So the two possible outcomes are either the box is vegan or it is not.

Population proportion = 4 / 12 ...*Since 4 are vegan out of
12*

= 0.333

X: no of vegan boxes (*considering out of 10)*

Expected value E(X) = np

Var V(x) = np(1-p)

*These are binomial distribution formulas*

Expected value E(X) = np

= 10 * 0.33

**E(X) = 3.333**

Var = np(1-p)

= 10 * 0.333 * 0.6667

Var = 2.2222

Sd =

**SD = 1.4907**

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