Q: If a random sample of 200 male Asian elephants is chosen, approximately how many would be expected to weigh less than 10,500 pounds?

$$200 \times 0.3247 = 64.94 \approx 65$$

Q: What is the standard deviation in the number of drivers who have had a parking ticket in a sample of 200, given $$p = 0.235$$?

$$\sqrt{200 \times 0.235 \times (1 - 0.235)} = 6.0$$

Question 1

Which of the following best describes a random variable?

Accepted Answer

A variable whose value is determined by the outcome of a random experiment.

Question 2

Which statement correctly distinguishes between discrete and continuous random variables?

Accepted Answer

Discrete random variables can only take specific, separate values, while continuous random variables can take any value within a range.

Question 3

Which of the following is NOT a condition required for the Central Limit Theorem (CLT) for the proportion?

Accepted Answer

The sample size must be greater than 30.

Question 4

A probability distribution is best defined as:

Accepted Answer

A function that assigns probabilities to each possible value of a random variable.

Question 5

Which scenario is an example of a binomial distribution?

Accepted Answer

Counting the number of students who pass a test out of 20, where each student has the same probability of passing.

Question 6

If two events are independent, what does this mean?

Accepted Answer

The occurrence of one event does not affect the probability of the other.

Question 7

A city survey finds the probability that a household owns at least 3 pets is 0.21. What is the probability that a randomly selected household owns 3 or more pets?

Accepted Answer

$$0.21$$

Question 8

Suppose a bag contains 12 red, 15 green, and 10 purple marbles. What is the probability that a randomly chosen marble is green?

Accepted Answer

$$\frac{15}{37} \approx 0.405$$

Question 9

In a binomial experiment with $$n = 17$$ and $$p = 0.235$$, what is the expected number of drivers who have had a parking ticket?

Accepted Answer

$$17 	imes 0.235 = 3.995$$

Question 10

The weight of male Asian elephants is normally distributed with mean $$\mu = 11,000$$ pounds and standard deviation $$\sigma = 1,100$$ pounds. What is the probability that a randomly chosen elephant weighs more than 14,000 pounds?

Accepted Answer

$$0.0032$$

Question 11

If a random sample of 200 male Asian elephants is chosen, approximately how many would be expected to weigh less than 10,500 pounds?

Accepted Answer

$$200 	imes 0.3247 = 64.94 \approx 65$$

Question 12

What is the standard deviation in the number of drivers who have had a parking ticket in a sample of 200, given $$p = 0.235$$?

Accepted Answer

$$\sqrt{200 	imes 0.235 	imes (1 - 0.235)} = 6.0$$

Question 13

Which of the following is true about mutually exclusive events?

Accepted Answer

They cannot occur at the same time.

Question 14

A sample of SMC students is asked if they own a car and how many hours per week they work. If one student is randomly selected, what is the probability that the student owns a car?

Accepted Answer

$$\frac{98}{201} \approx 0.488$$

Question 15

For the sampling distribution of the mean weight of male Asian elephants, if a sample of 40 is chosen, what is the standard error?

Accepted Answer

$$\frac{1100}{\sqrt{40}} \approx 174$$

Question 16

Which of the following is NOT a requirement for the CLT for the mean?

Accepted Answer

The sample mean must equal the population mean.

Question 17

A newspaper claims 35% of residents have a college degree. In a sample of 300, what is the standard error of the proportion?

Accepted Answer

$$\sqrt{\frac{0.35 	imes 0.65}{300}} \approx 0.028$$

Question 18

If 12% of SMC students plan to pursue a medical job, what is the minimum sample size required for the CLT for the proportion to apply?

Accepted Answer

$$n = 95$$

Question 19

In a binomial experiment with $$n = 17$$ and $$p = 0.235$$, what is the probability that exactly 6 drivers have had a parking ticket?

Accepted Answer

$$0.109$$

Step-by-Step Guidance for Introductory Statistics Review Problems (Chapters 5–8)

Study Guide - Practice Questions

Study Guide - Flashcards