State whether each of the following random variables is discrete or continuous:(

Question

State whether each of the following random variables is discrete or continuous:(a) The number of defective tires on a car

DiscreteContinuous    

(b) The weight of a cat

DiscreteContinuous    

(c) The number of letters in a word

DiscreteContinuous    

(d) The number of draws (with replacement) from a deck of cards until a heart is selected

DiscreteContinuous    

(e) The length of a movie

DiscreteContinuous   

Statistical Tables 860 Table 1 Random Numbers 860 Table 2 Standard Normal Probabilities (Cumulative z Curve Areas) 862 Table 3 t Critical Values 864 Table 4 Tail Areas for t Curves 865 Table 5 Curves of b 5 P(Type II Error) for t Tests 868 Table 6 Values That Capture Specifi ed Upper-Tail F Curve Areas 869 Table 7 Critical Values of q for the Studentized Range Distribution 873 Table 8 Upper-Tail Areas for Chi-Square Distributions 874 Table 9 Binomial Probabilities 876

Explanation / Answer

Discrete variables are countable in a finite amount of time. For example, you can count the change in your pocket. You can count the money in your bank account. You could also count the amount of money in everyone’s bank account. It might take you a long time to count that last item, but the point is — it’s still countable.

Continuous Variables would (literally) take forever to count. In fact, you would get to “forever” and never finish counting them. For example, take age. You can’t count “age”. Why not? Because it would literally take forever. For example, you could be:
25 years, 10 months, 2 days, 5 hours, 4 seconds, 4 milliseconds, 8 nanoseconds, 99 picosends…and so on. You could turn age into a discrete variable and then you could count it. For example:

a) Discrete as we can count

b) weight is continuous.

c) Discrete as it is finite

d) continuous. it could take infinite trials or draws

e) The individual is a movie. Length is a continuous variable having values in the range 0 to 250 min. The lower limit will of course be somewhat larger than 0 and the upper limit could exceed 250 min.

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