Q: A quiz has three questions: the first is True/False, the second has four choices (A/B/C/D), and the third has three choices (Yes/No/Maybe). How many possible response sets are there?

There are $$2 \times 4 \times 3 = 24$$ possible response sets.

Question 1

A soda can has a volume of 12.10 ounces. Given the average volume is 11.98 ounces and the standard deviation is 0.03 ounces, what is the z-score for this can? Is this value considered unusual?

Accepted Answer

The z-score is $$z = \frac{12.10 - 11.98}{0.03} = 4$$, which is considered unusually high.

Question 2

A soda can has a z-score of $$-1.33$$ given the mean is $$11.98$$ ounces and the standard deviation is $$0.03$$ ounces. What is the volume of this can?

Accepted Answer

The volume is $$11.94$$ ounces.

Question 3

Which is more extreme: a soda can with $$12.02$$ ounces (mean $$11.98$$, SD $$0.03) or a $$tea bottle with $$16.80$$ ounces (mean $$16.87$$, SD $$0.04$$)?

Accepted Answer

The tea bottle is more extreme because its z-score is further from zero.

Question 4

Given the data set: $$12, 15, 19, 24, 40, 42, 44, 49, 50, 51$$, what is the Interquartile Range (IQR)?

Accepted Answer

The IQR is $$49 - 19 = 30.$$

Question 5

In the same data set, what is the percentile of the value $$24$$?

Accepted Answer

$$24 is at $$the $$30th $$percentile.

Question 6

A quiz has three questions: the first is True/False, the second has four choices (A/B/C/D), and the third has three choices (Yes/No/Maybe). How many possible response sets are there?

Accepted Answer

There are $$2 	imes 4 	imes 3 = 24$$ possible response sets.

Question 7

In a standard deck of 52 cards, what is the probability that a randomly selected card is a King or a 7?

Accepted Answer

The probability is $$\frac{8}{52}.$$

Question 8

A fair coin is tossed four times. What is the probability of getting exactly two heads and two tails?

Accepted Answer

The probability is $$\frac{6}{16}.$$

Question 9

A bag contains 20 marbles: 4 red, 6 green, 7 blue, and 3 white. If two marbles are drawn without replacement, what is the probability that both are green?

Accepted Answer

The probability is $$\frac{30}{380}.$$

Question 10

Given the probability distribution: $$P(X=0)=0.4$$, $$P(X=1)=0.25$$, $$P(X=2)=0.2$$, $$P(X=3)=0.1$$, $$P(X=4)=0.05$$, what is the mean ($$\mu) of$$ $$X$$?

Accepted Answer

The mean is $$\mu = 1.1.$$

Question 11

What are the four requirements for a binomial distribution?

Accepted Answer

Fixed number of trials, only two outcomes per trial, trials are independent, same probability of success in each trial.

Question 12

In a survey of 500 people, 100 are in group A. What is the probability that a randomly selected person is in group A?

Accepted Answer

The probability is $$\frac{100}{500}.$$

Question 13

Suppose 10 U.S. adults are selected at random, and 11% are left-handed. What is the probability that none of them are left-handed?

Accepted Answer

The probability is $$(0.89)^{10}$$ \approx 0.312$$.

Question 14

For the same scenario, what is the mean and standard deviation of the number of left-handed people out of 10?

Accepted Answer

Mean $$\mu = np = 10 	imes 0.11 = 1.1$$, Standard deviation $$\sigma = \sqrt{npq} = \sqrt{10 	imes 0.11 	imes 0.89} \approx 0.989$$

Question 15

In the probability distribution $$P(X=0)=0.4$$, $$P(X=1)=0.25$$, $$P(X=2)=0.2$$, $$P(X=3)=0.1$$, $$P(X=4)=0.05$$, what is $$P(X 
eq 2)$$?

Accepted Answer

$$P(X 
eq 2) = 1 - 0.2 = 0.8$$

Question 16

A fair coin is tossed four times. What is the probability of getting at least one head?

Accepted Answer

The probability is $$\frac{15}{16}.$$

Question 17

In a deck of 52 cards, what is the probability that a randomly selected card is black or a King?

Accepted Answer

The probability is $$\frac{28}{52}.$$

Question 18

In the marble problem, what is the probability that one marble is red and one is blue (order does not matter)?

Accepted Answer

The probability is $$\frac{28}{190}.$$

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