Q: If two events $$A$$ and $$B$$ are independent, which of the following is true?

$$P(A \cap B) = P(A) \times P(B)$$

Question 1

Which of the following best describes the mean of a data set?

Accepted Answer

The sum of all values divided by the number of values.

Question 2

A researcher collects the following data set: 2, 4, 4, 6, 8. What is the median?

Accepted Answer

$$4$$

Question 3

Which of the following is the correct formula for the sample variance $$s^2 of$$ $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 4

Suppose the heights of adult men in a city are normally distributed with mean $$\mu = 70$$ inches and standard deviation $$\sigma = 3$$ inches. What is the $$z-$$score for a man who is 76 inches tall?

Accepted Answer

$$z = 2$$

Question 5

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 6

Which of the following statements about the standard normal distribution is TRUE?

Accepted Answer

It has a mean of $$0$$ and a standard deviation of $$1.$$

Question 7

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 8

A sample of 10 exam scores has a mean of 80 and a standard deviation of 5. What is the variance?

Accepted Answer

$$25$$

Question 9

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

Accepted Answer

It is always skewed to the left.

Question 10

A researcher wants to estimate the average weight of apples in an orchard. Which sampling method is most likely to produce a representative sample?

Accepted Answer

Randomly selecting apples from all trees in the orchard.

Question 11

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$ and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 12

Which of the following best describes the mode of a data set?

Accepted Answer

The value that appears most frequently.

Question 13

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What percentage of data falls within one standard deviation of the mean?

Accepted Answer

$$68\%$$

Question 14

Which of the following is the correct formula for the $$z-$$score of a value $$x in a $$normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 15

A hospital records the blood types of 100 patients. Which type of variable is blood type?

Accepted Answer

Qualitative, categorical

Question 16

If the probability of rain tomorrow is $$0.3$$, what is the probability that it will NOT rain?

Accepted Answer

$$0.7$$

Question 17

Which of the following is an example of a continuous variable?

Accepted Answer

Height of a person

Question 18

A boxplot is useful for displaying which of the following?

Accepted Answer

The distribution of a data set, including median and quartiles

Question 19

Which of the following best describes the range of a data set?

Accepted Answer

The difference between the highest and lowest values

Question 20

A researcher wants to test if a new drug lowers blood pressure. Which is the null hypothesis?

Accepted Answer

The new drug has no effect on blood pressure.

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