AP Statistics : How to find mean of a random variable

Study concepts, example questions & explanations for AP Statistics

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Example Questions

Example Question #4 : Random Variables

Let us suppose you are a waiter. You work your first four shifts and receive the following in tips: (1) 20, (2) 30, (3) 15, (4) 5. What is the mean amount of tips you will receive in a given day?

Possible Answers:

Correct answer:

Explanation:

The answer is 17.5. Simply take the values for each day, add them, and divide by the total number of days to obtain the mean: 

Example Question #1 : How To Find Mean Of A Random Variable

Robert's work schedule for next week will be released today.  Robert will work either 45, 40, 25, or 12 hours.  The probabilities for each possibility are listed below:

45 hours: 0.3

40 hours: 0.2

25 hours: 0.4

12 hours: 0.1

What is the mean outcome for the number of hours that Robert will work?

Possible Answers:

Correct answer:

Explanation:

We are required to find the mean outcome where the probability of each possible result varies--the random/weighted mean.  First, multiply each possible outcome by the probability of that outcome occurring.  Second, add these results together. 

 

 

Example Question #11 : Random Variables

There are  collectable coins in a bag.  are  ounces,  are  ounces,  are  ounces, and  are  ounces. If one coin is randomly selected, what is the mean possible weight in ounces?

Possible Answers:

Correct answer:

Explanation:

We are required to find the mean outcome where the probability of each possible result varies--the random/weighted mean. 

First, multiply each possible outcome by the probability of that outcome occurring. 

Second, add these results together. 

 

Example Question #71 : Statistical Patterns And Random Phenomena

A basketball player makes  of his three-point shots. If he takes  three-point shots each game, how many points per game does he score from three-point range?

Possible Answers:

Correct answer:

Explanation:

First convert .

The player's three-point shooting follows a binomial distribution with  and .

On average, he thus makes  three-point shots per game.

This means he averages 12 points per game from three-point range if he tries to make 10 three-pointers per game.

Example Question #13 : Random Variables

Tim samples the average plant height of potato plants for his science class and finds the following distribution (in inches):

Which of the following is/are true about the data?

i: the mode is 

ii: the mean is 

iii: the median is 

iv: the range is 

Possible Answers:

i, ii & iii

ii, iii & iv

i & ii

all of the above

i & iii

Correct answer:

i & ii

Explanation:

Analyzing the data, there are more 6s than anything else (mode), the median is between  and     , the mean is , and the range is 

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