Question

Classify the random variables below according to whether they are discrete or continuous.a. The number of people in a restaurant that has a capacity of 100.b. The height of a randomly selected giraffe.c. The square footage of a house.d. The number of light bulbs that burn out in the next week in a room with 10 bulbs.e. The number of points scored during a basketball game.

Answer 1

a) Discrete

b) Continuous

c) Continuous

d) Discrete

e)Discrete

Explanation:

Continuous:

Real numbers, can be integer, decimal, etc.

Discrete:

Only integer(countable values). So can be 0,1,2...

a. The number of people in a restaurant that has a capacity of 100.

You cannot have half a person, for example.

The possible number of people in the restaurant are 0, 1, 2,..., 100. So this variable is discrete.

b. The height of a randomly selected giraffe.

The giraffe can have half a meter, for example. That is, the height can be a decimal number. So this variable is continuous

c. The square footage of a house.

You can have half a square, for example. So this variable is continuous.

d. The number of light bulbs that burn out in the next week in a room with 10 bulbs.

Possible values: 0 bulbs, 1 bulb, ..., 10 bulbs

Only countable values.

So discrete

e. The number of points scored during a basketball game.

0 points, 1 point, 2 points, 10 points, ...

There are no half points in basketball.

So discrete