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AP Statistics : How to find mean of a random variable

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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:

$\$20$

$\$17$

$\$17.50$

$\$30$

Correct answer:

$\$17.50$

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: $\frac{20+30+15+5}{4}$

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Example Question #3 : Random Variables

There are 100 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:

4.9

5.3

1.51

Correct answer:

4.9

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.

$(0.4\cdot 3)+(0.1\cdot 5)+(0.3\cdot 6)+(0.2\cdot 7)=4.9$

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Example Question #71 : Statistical Patterns And Random Phenomena

A basketball player makes $40\%$ 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 $40\% \rightarrow 0.40$ .

The player's three-point shooting follows a binomial distribution with n = 10 and p = 0.4 .

On average, he thus makes $np = 10\cdot 0.4 = 4$ 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.

4(3)=12

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Example Question #11 : Random Variables

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

4,4,5,5,6,6,6,6,6,7,7,7,8,9,10,10,12,14

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

i: the mode is

ii: the mean is 7.33333

iii: the median is

iv: the range is

Possible Answers:

all of the above

i & iii

i, ii & iii

i & ii

ii, iii & iv

Correct answer:

i & ii

Explanation:

Analyzing the data, there are more 6s than anything else (mode), the median is between and (6.5) , the mean is 132/18=7.33333 , and the range is 14-4=10

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Example Question #71 : Probability

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:

31.6

30.5

122

0.25

32.7

Correct answer:

32.7

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.

$(45\cdot 0.3) + (40\cdot 0.2) + (25\cdot 0.4) + (12\cdot 0.1) = 32.7$

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AP Statistics : How to find mean of a random variable

Study concepts, example questions & explanations for AP Statistics

All AP Statistics Resources

Example Questions

Example Question #4 : Random Variables

Example Question #3 : Random Variables

Example Question #71 : Statistical Patterns And Random Phenomena

Example Question #11 : Random Variables

Example Question #71 : Probability

All AP Statistics Resources

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