Q: In a probability distribution, the probability that a randomly selected patient recovers from a treatment is 0.7. What is the probability that two randomly selected patients both recover, assuming independence?

$$P(\text{both recover}) = 0.7 \times 0.7 = 0.49$$

Question 1

A researcher wants to study the average height of all adult women in a city. She randomly selects 200 women and measures their heights. In this scenario, which statement best describes the sample and the population?

Accepted Answer

The sample is the 200 women measured; the population is all adult women in the city.

Question 2

Which of the following is an example of quantitative data?

Accepted Answer

The number of books read by each student in a month

Question 3

A histogram of exam scores shows most scores clustered on the left with a long tail extending to the right. How would you describe the shape of this distribution?

Accepted Answer

Skewed right

Question 4

Given the data set: 4, 7, 8, 10, 12. What is the mean?

Accepted Answer

Mean $$= \frac{4+7+8+10+12}{5} = \frac{41}{5} = 8.2$$

Question 5

Given the data set: 3, 5, 7, 9, 11, what is the median?

Accepted Answer

Median $$= 7$$

Question 6

A boxplot shows the following values: minimum = 10, Q1 = 15, median = 20, Q3 = 25, maximum = 30. Which value represents the third quartile?

Accepted Answer

Q3 = 25

Question 7

In a probability distribution, the probability that a randomly selected patient recovers from a treatment is 0.7. What is the probability that two randomly selected patients both recover, assuming independence?

Accepted Answer

$$P(	ext{both recover}) = 0.7 	imes 0.7 = 0.49$$

Question 8

A normal distribution has mean $$\mu = 50$$ and standard deviation $$\sigma = 10. $$What is the z-score for $$x = 65$$?

Accepted Answer

$$z = \frac{65 - 50}{10} = \frac{15}{10} = 1.5$$

Question 9

A student scores 80 on a test where the mean is 70 and the standard deviation is 5. What percentile does this score correspond to in a normal distribution?

Accepted Answer

First, calculate $$z = \frac{80 - 70}{5} = 2. $$Using the z-table, $$z = 2$$ corresponds to approximately the 97.5th percentile.

Question 10

Which of the following best describes the five-number summary in a boxplot?

Accepted Answer

Minimum, Q1, Median, Q3, Maximum

Question 11

A hospital records the blood types of 100 patients. Is this data categorical or quantitative?

Accepted Answer

Categorical

Question 12

A probability distribution for the number of defective items in a batch is given as: $$P(X=0)=0.6$$, $$P(X=1)=0.3$$, $$P(X=2)=0.1. $$What is the probability that there is at least one defective item?

Accepted Answer

$$P(X \geq 1) = P(X=1) + P(X=2) = 0.3 + 0.1 = 0.4$$

Question 13

A data set has values: 2, 4, 6, 8, 10. What is the median?

Accepted Answer

Median $$= 6$$

Question 14

A company wants to estimate the average salary of its employees. It surveys 50 randomly selected employees. Which term best describes the group of all employees at the company?

Accepted Answer

Population

Question 15

A histogram of daily temperatures in July shows a peak in the middle and tails on both sides. Which description best fits this distribution?

Accepted Answer

Symmetric

Question 16

A normal distribution has $$\mu = 100$$ and $$\sigma = 15. $$What is the z-score for $$x = 85$$?

Accepted Answer

$$z = \frac{85 - 100}{15} = \frac{-15}{15} = -1$$

Question 17

A boxplot for cholesterol levels shows the minimum at 120, Q1 at 150, median at 180, Q3 at 210, and maximum at 240. What is the interquartile range (IQR)?

Accepted Answer

IQR $$= Q3 - Q1 = 210 - 150 = 60$$

Question 18

A survey records the favorite sports of 500 students. Is this data categorical or quantitative?

Accepted Answer

Categorical

Question 19

A probability distribution for the number of accidents per day is: $$P(X=0)=0.5$$, $$P(X=1)=0.3$$, $$P(X=2)=0.2. $$What is the expected number of accidents per day?

Accepted Answer

Expected value $$= 0 	imes 0.5 + 1 	imes 0.3 + 2 	imes 0.2 = 0 + 0.3 + 0.4 = 0.7$$

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