How to find mean of a random variable

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AP Statistics › How to find mean of a random variable

Questions 1 - 5

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?

$\$17.50$

$\$20$

$\$30$

$\$17$

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

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?

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.

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

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

i & ii

i & iii

i, ii & iii

all of the above

ii, iii & iv

Explanation

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

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?

Explanation

First convert $40% \rightarrow 0.40$ .

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

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.

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?