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

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 #1 : How To Find Mean Of A Random Variable

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:

all of the above

ii, iii & iv

i & ii

i, ii & iii

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 

Example Question #71 : Statistical Patterns And Random Phenomena

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. 

 

 

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