Question

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random varialbe.

a) Is the number of people in a restuarant that has a capacity of 300 discrete or continuous?

A) The random variable is continuous. The possilbe values are x=0,1,2,....,300

B) The random variable is continuous. The possible values are 0 less than or equal to x less than or equal to 300

C) The random variable is discrete. The possible values are 0 less than or equal to x less than or equal to 300.

D) The random variable is discrete. The possible values are x=0,1,2,...,300

b) Is the amount of snowfall discrete or continuous?

A) The random variable is discrete. The possible values are s greater than or equal to 0

B) The random variable is continuous. The possible values are s=1,2,3,....

C) The random variable is continuous. The possible values are s greater than or equal to 0

D) The random variable is discrete. The possible values are s=1,2,3, ....

Answer 1

(a)Discrete Variable (Option D)

(b)Continuous Variable (Option C)

Explanation:

A Discrete Variable is a variable that can only take on a finite number of values. All qualitative variables are discrete.

A continuous variable on the other hand is a variable that can take on values over a non-empty range of the real numbers.

(a)The number of people in a restaurant is a discrete variable and the possible values are x=0,1,2,...,300. You cannot have 0.5 persons in a restaurant.

(b)The amount of snowfall is a continuous variable and the values of the amount of snowfall, s could take on any real value greater than or equal to zero.