) A teacher collected data on the number of pencils used by students in a month. The data is:

Question

2, 3, 4, 5, 6, 100

Which measure of center is the best representation of the typical number of pencils used?
(4 Points)

Mean

Median

Mode

Range
20
(7.SP.C.5) A jar contains 3 red marbles, 5 blue marbles, and 2 green marbles. A student randomly selects one marble.

Which statement best describes the likelihood of drawing a blue marble?
(4 Points)

It is certain that a blue marble will be drawn.

It is unlikely that a blue marble will be drawn.

It is equally likely to draw a blue or red marble.

It is more likely to draw a blue marble than any other color.
21
(7.SP.C.5) A student is playing a game with two spinners:


Spinner A has 4 equal sections: red, blue, green, yellow.


Spinner B has 8 equal sections: red, blue, green, yellow, orange, purple, white, black.


The student wins if they spin red.

Which statement best compares the probabilities of winning on Spinner A vs. Spinner B?
(4 Points)

The probability of spinning red is the same for both spinners.

It is more likely to spin red on Spinner A than on Spinner B.

It is more likely to spin red on Spinner B than on Spinner A.

It is impossible to spin red on either spinner.
22
(7.SP.C.6) A student flips a coin 100 times and records the number of times it lands on heads. She gets heads 42 times.

Based on this experiment, what is the experimental probability of flipping heads?
(4 Points)

0.42

0.50

0.58

0.75
23
(7.SP.C.6) A six-sided die is rolled 60 times in an experiment. The results are:


1: 8 times


2: 12 times


3: 10 times


4: 10 times


5: 9 times


6: 11 times


How does the experimental probability of rolling a 1 compare to the theoretical probability?
(4 Points)

The experimental probability (8/60) is less than the theoretical probability (1/6).

The experimental probability (8/60) is equal to the theoretical probability (1/6).

The experimental probability (8/60) is greater than the theoretical probability (1/6).

There is no way to compare experimental and theoretical probability.
24
(7.SP.C.7) A basketball player makes 75% of her free throws. She is about to take four free throws in a row.

Which simulation would best represent the probability of her making each free throw?
(4 Points)

Rolling a six-sided die and counting outcomes of 1, 2, 3, or 4 as a made shot.

Flipping a coin, with heads representing a made shot.

Spinning a spinner divided into four equal sections and counting three of them as made shots.

Drawing a card from a standard deck and counting red cards as made shots.

Answer 1

Here are the answers to each question based on the information provided:

Question 1: Best measure of center for the number of pencils used (2, 3, 4, 5, 6, 100)
The best measure of center in this case is the Median. The presence of the outlier (100) heavily skews the mean, making it not representative of the typical usage. The median (the middle value when the data is ordered) is 4, which better reflects the typical number of pencils used by the majority of students.

Question 2: Likelihood of drawing a blue marble from the jar (3 red, 5 blue, 2 green)
The statement that best describes the likelihood of drawing a blue marble is: It is more likely to draw a blue marble than any other color. There are 5 blue marbles out of a total of 10 marbles, making the probability of drawing a blue marble 50%, which is higher than the probabilities for red (30%) and green (20%).

Question 3: Comparing probabilities of winning on Spinner A vs. Spinner B
The correct statement is: It is more likely to spin red on Spinner A than on Spinner B. Spinner A has a 25% chance (1 in 4 sections is red), while Spinner B has a 12.5% chance (1 in 8 sections is red).

Question 4: Experimental probability of flipping heads (42 heads out of 100 flips)
The experimental probability is: 0.42. This is calculated by dividing the number of heads (42) by the total number of flips (100).

Question 5: Comparing experimental probability of rolling a 1 to theoretical probability
The correct comparison is: The experimental probability (8/60) is less than the theoretical probability (1/6). The theoretical probability of rolling a 1 on a fair die is 1/6, which is approximately 0.1667. The experimental probability of rolling a 1 is 8/60, which simplifies to approximately 0.1333, thus it is less.

Question 6: Best simulation for estimating the probability of making free throws (75%)
The best simulation would be: Rolling a six-sided die and counting outcomes of 1, 2, 3, or 4 as a made shot. This is because rolling a 4 out of 6 outcomes (which is 67%) and counting two outcomes (which is a 33%) can closely simulate the probability of making around 75% of shots, adjusting for practical purposes a bit from 4 successful rolls.

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