Q: A game is played with a 6-sided die. If the die shows 1, the player wins $$35; otherwise, they win nothing. If it costs 7 to $$play, what is the expected value of the game?

$$\left(\frac{1}{6} \times 35\right) + \left(\frac{5}{6} \times 0\right) - 7 = -1.17$$

Q: In a normal distribution of car prices with mean $$19,000 and standard deviation 2$$,000, what price is two standard deviations above the mean?

$$19,000 + 2 \times 2,000 = 23,000$$

Question 1

A 10-sided die is rolled. What is the probability of rolling an even number?

Accepted Answer

$$\frac{5}{10}$$

Question 2

If you are dealt one card from a standard 52-card deck, what is the probability of being dealt a face card?

Accepted Answer

$$\frac{12}{52}$$

Question 3

A spinner is divided into 4 equal colored regions: red, yellow, green, and blue. If the pointer is spun once, what is the probability it lands in a region that is red or yellow?

Accepted Answer

$$\frac{2}{4}$$

Question 4

Given the frequency table for ages at inauguration, what is the total number of presidents represented?

Accepted Answer

$$44$$

Question 5

Using the histogram provided, which age group had the highest frequency of presidents at inauguration?

Accepted Answer

56-60

Question 6

If a donut is selected at random from a box containing 2 jelly-filled, 5 lemon-filled, and 17 custard-filled donuts, what is the probability of selecting a custard-filled donut on the first try?

Accepted Answer

$$\frac{17}{24}$$

Question 7

A game is played with a 6-sided die. If the die shows 1, the player wins $$35; otherwise, they win nothing. If it costs 7 to $$play, what is the expected value of the game?

Accepted Answer

$$\left(\frac{1}{6} 	imes 35ight) + \left(\frac{5}{6} 	imes 0ight) - 7 = -1.17$$

Question 8

In a normal distribution of car prices with mean $$19,000 and standard deviation 2$$,000, what price is two standard deviations above the mean?

Accepted Answer

$$19,000 + 2 	imes 2,000 = 23,000$$

Question 9

Given the grouped frequency distribution for ages at inauguration, does the data appear to be normally distributed?

Accepted Answer

No, the data is not symmetric and does not appear normally distributed.

Question 10

If a person is selected at random from a group of 6 male professors, 8 female professors, 5 male teaching assistants, and 13 female teaching assistants, what is the probability that the selected person is a professor or male?

Accepted Answer

$$\frac{19}{32}$$

Question 11

A standard deck of 52 cards is used. What is the probability of being dealt a jack or a seven?

Accepted Answer

$$\frac{8}{52}$$

Question 12

If the mean of the data set $$\{72, 69, 71, 64, 69, 75\} is $$calculated, what is the result?

Accepted Answer

$$\frac{420}{6} = 71$$

Question 13

In the context of probability, what does it mean if an event has a probability of 0?

Accepted Answer

The event is impossible.

Question 14

If a spinner with 4 equal regions is spun three times, what is the probability it lands on green every time?

Accepted Answer

$$\left(\frac{1}{4}\$$right)^3$$ = \frac{1}{64}$$

Question 15

If the standard deviation of car prices is $$2,000, what percentage of buyers paid between 17$$,000 and $21,000 according to the 68-95-99.7 rule?

Accepted Answer

$$68\%$$

Question 16

What is misleading about a visual display of data where the years on the x-axis are not evenly spaced?

Accepted Answer

It distorts the perception of trends over time.

Grouped Frequency Distribution and Histogram Analysis

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