Q: If the probability of rain tomorrow is 0.2, what is the probability that it will NOT rain?

$$P(\text{not rain}) = 1 - 0.2 = 0.8$$

Question 1

A pharmaceutical company tests a new drug and finds a p-value of 0.03 when comparing it to a placebo. Which statement best describes the statistical significance of this result?

Accepted Answer

The result is statistically significant because the p-value is less than 0.05.

Question 2

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

Accepted Answer

The distribution is skewed to the right.

Question 3

A dataset of students' test scores has a mean of 75 and a standard deviation of 10. What is the z-score for a student who scored 95?

Accepted Answer

$$z = \frac{95 - 75}{10} = 2$$

Question 4

According to the 68-95-99.7 rule, what percentage of values lie within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 5

A researcher collects 100 random samples of size 30 from a population. According to the Central Limit Theorem, what will the distribution of the sample means look like?

Accepted Answer

It will be approximately normal, regardless of the population's distribution.

Question 6

If the probability of rain tomorrow is 0.2, what is the probability that it will NOT rain?

Accepted Answer

$$P(	ext{not rain}) = 1 - 0.2 = 0.8$$

Question 7

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

Accepted Answer

$$P = \frac{2}{6} = \frac{1}{3}$$

Question 8

Which statement best describes the law of large numbers?

Accepted Answer

As the number of trials increases, the sample mean approaches the population mean.

Question 9

A gambler believes that after losing five coin tosses in a row, the next toss is more likely to be heads. This belief is an example of:

Accepted Answer

The gambler's fallacy

Question 10

If the expected value of a lottery ticket is $$-\0.50$, what does this mean?

Accepted Answer

On average, you lose $0.50 per ticket purchased.

Question 11

Which of the following best describes a positive correlation?

Accepted Answer

As one variable increases, the other variable also increases.

Question 12

A scatterplot shows a strong negative linear relationship between hours spent watching TV and exam scores. What is the likely value of the correlation coefficient $$r$$?

Accepted Answer

$$r \approx -0.8$$

Question 13

Which of the following statements about outliers in correlation analysis is TRUE?

Accepted Answer

Outliers can significantly affect the value of the correlation coefficient.

Question 14

A group of students is divided into two groups based on their study habits. The correlation between hours studied and exam scores is calculated for each group. What is this an example of?

Accepted Answer

Interpreting correlations involving grouped data.

Question 15

Which equation represents the best-fit line (regression line) for predicting $$y$$ from $$x$$?

Accepted Answer

$$y = a + bx$$

Question 16

A regression analysis finds the best-fit line for predicting weight from height as $$	ext{weight} = 50 + 2 	imes 	ext{height}. $$What is the predicted weight for a person who is 70 inches tall?

Accepted Answer

$$50 + 2 	imes 70 = 190$$

Question 17

A population has a mean of 100 and a standard deviation of 15. What is the probability that a randomly selected value falls between 85 and 115, assuming a normal distribution?

Accepted Answer

About 68%, according to the 68-95-99.7 rule.

Question 18

A hospital records the number of patients admitted each day. The data is heavily skewed. If the hospital takes random samples of size 40, what does the Central Limit Theorem predict about the distribution of sample means?

Accepted Answer

The sample means will be approximately normally distributed.

Question 19

A student scores at the 90th percentile on a standardized test. What does this mean?

Accepted Answer

The student scored higher than 90% of the test takers.

Key Concepts in Normal Distribution, Probability, and Correlation

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