Q: A medical test for a disease has a sensitivity of 90% and a specificity of 95%. If the disease prevalence is 2%, what is the probability that a randomly selected person tests positive?

$$0.02 \times 0.90 + 0.98 \times 0.05 = 0.067$$

Q: If $$P(A|B) = 0.4$$, $$P(B) = 0.2$$, and $$P(A) = 0.1$$, what is $$P(B|A)$$ according to Bayes' Theorem?

$$P(B|A) = \frac{P(A|B) \cdot P(B)}{P(A)} = \frac{0.4 \times 0.2}{0.1} = 0.8$$

Question 1

A hospital administrator wants to summarize the number of patients admitted each day for a month. Which statistical tool is most appropriate for organizing this data?

Accepted Answer

Frequency distribution

Question 2

Which of the following best describes a histogram?

Accepted Answer

A graph that displays quantitative data using bars whose heights represent frequencies

Question 3

A misleading graph might use a vertical axis that does not start at zero. What is the likely effect of this manipulation?

Accepted Answer

It exaggerates differences between data values

Question 4

A researcher plots the heights and weights of 100 athletes. Which graph should they use to best visualize the relationship between these two variables?

Accepted Answer

Scatterplot

Question 5

If the mean of a dataset is $$\ 50$, the median is $$\$$ 45$$, and the mode is $$\ 40$, what can you infer about the shape of the distribution?

Accepted Answer

The distribution is skewed to the right

Question 6

Which measure of variation is calculated as $$\ s$$ = \sqrt{\frac{\sum (x_i - \bar{x}$$)^2$$}{n-1}} \$ ?

Accepted Answer

Standard deviation

Question 7

A student scores 85 on a test where the mean is 80 and the standard deviation is 5. What is the student's z-score?

Accepted Answer

$$z = \frac{85 - 80}{5} = 1$$

Question 8

Which of the following is NOT a property of a boxplot?

Accepted Answer

It shows the mean

Question 9

If a fair coin is tossed three times, what is the probability of getting exactly two heads?

Accepted Answer

$$\frac{3}{8}$$

Question 10

A deck of cards contains 52 cards. What is the probability of drawing either a heart or a king?

Accepted Answer

$$\frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52}$$

Question 11

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.15$$

Question 12

A medical test for a disease has a sensitivity of 90% and a specificity of 95%. If the disease prevalence is 2%, what is the probability that a randomly selected person tests positive?

Accepted Answer

$$0.02 	imes 0.90 + 0.98 	imes 0.05 = 0.067$$

Question 13

If $$P(A|B) = 0.4$$, $$P(B) = 0.2$$, and $$P(A) = 0.1$$, what is $$P(B|A)$$ according to Bayes' Theorem?

Accepted Answer

$$P(B|A) = \frac{P(A|B) \cdot P(B)}{P(A)} = \frac{0.4 	imes 0.2}{0.1} = 0.8$$

Question 14

How many ways can a committee of 3 people be chosen from a group of 10?

Accepted Answer

$$\frac{10!}{3! \cdot 7!} = 120$$

Question 15

A simulation is used to estimate the probability of a rare event. Which of the following is a key advantage of using simulation?

Accepted Answer

It allows estimation when analytical calculation is difficult

Question 16

A boxplot shows a data set with a long upper whisker and several points above the upper quartile. What does this indicate?

Accepted Answer

The data is skewed to the right with possible outliers

Question 17

Which of the following is the formula for the variance of a sample?

Accepted Answer

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

Question 18

A scatterplot of two variables shows a strong positive linear relationship. Which value is most likely for the correlation coefficient $$r$$?

Accepted Answer

$$r = 0.90$$

Question 19

A company wants to compare the salaries of employees in two departments. Which statistical graph would best show the distribution and identify outliers in each department?

Accepted Answer

Boxplot

Study Guide: Exploring Data, Descriptive Statistics, and Probability

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