Q: Which formula is used to calculate the probability of two independent events A and B both occurring?

$$P(A \text{ and } B) = P(A) \times P(B)$$

Question 1

Which of the following best describes the shape of a normal distribution?

Accepted Answer

A symmetric, bell-shaped curve

Question 2

Given a data set with values: 2, 4, 6, 8, 10, what is the mean?

Accepted Answer

$$\frac{2+4+6+8+10}{5} = 6$$

Question 3

If the median of a data set is 15, which statement is true?

Accepted Answer

Half the values are less than 15 and half are greater than 15

Question 4

Which formula is used to calculate the standard deviation of a sample?

Accepted Answer

$$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}$$

Question 5

A boxplot is used to display which of the following?

Accepted Answer

The spread and center of a data set, including quartiles and outliers

Question 6

If a histogram of adult heights is approximately symmetric, what does this suggest about the distribution?

Accepted Answer

The mean and median are likely to be similar

Question 7

Which of the following is NOT a property of the normal distribution?

Accepted Answer

It is always skewed to the right

Question 8

Given a z-score formula $$z = \frac{x - \mu}{\sigma}$$, what does a z-score of 2.0 mean?

Accepted Answer

The value $$x is $$two standard deviations above the mean

Question 9

If the probability of an event is $$P(A) = 0.25$$, what is the probability that the event does NOT occur?

Accepted Answer

$$1 - 0.25 = 0.75$$

Question 10

Which of the following best describes the concept of 'outlier' in a data set?

Accepted Answer

A value that is much higher or lower than most of the other values

Question 11

A student scores 1.5 standard deviations above the mean on a test. What is their z-score?

Accepted Answer

$$z = 1.5$$

Question 12

If a data set is skewed to the left, which of the following is most likely true?

Accepted Answer

The mean is less than the median

Question 13

Which formula is used to calculate the probability of two independent events A and B both occurring?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 14

A college student’s time spent studying is normally distributed with mean $$\mu = 10$$ hours and standard deviation $$\sigma = 2$$ hours. What is the probability that a randomly selected student studies more than 14 hours?

Accepted Answer

Approximately $$0.0228$$

Question 15

Which of the following is a real-world example of a binomial experiment?

Accepted Answer

Flipping a coin 10 times and counting the number of heads

Question 16

If the interquartile range (IQR) of a data set is 12, what does this represent?

Accepted Answer

The spread of the middle 50% of the data

Question 17

Which formula is used to find the probability of at least one event occurring in a binomial experiment with $$n$$ trials and probability $$p$$?

Accepted Answer

$$P(	ext{at least one}) = 1 - (1-p)^n$$

Question 18

A histogram shows the frequency of values in a data set. What does a bar in the histogram represent?

Accepted Answer

The number of data values within a specific interval

Question 19

If a data set has a mean of 50 and a standard deviation of 5, what is the z-score for a value of 60?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 20

Which of the following best describes the purpose of using a stem-and-leaf plot?

Accepted Answer

To display the distribution of data while preserving the original values

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