Q: A club has 12 members. In how many ways can a president, vice president, and secretary be selected (no person holds more than one office)?

$$12 \times 11 \times 10 = 1320$$

Q: A student guesses on 8 true/false questions. Let $$X be $$the number of questions answered correctly. What is the probability that the student gets exactly 6 correct? (Assume $$p = 0.5$$ for a correct answer.)

$$\binom{8}{6} (0.5)^8$ = 28 \times 0.00390625 = 0.109375$$

Q: A basketball player makes free throws with probability $$p = 0.80. $$Suppose the player attempts $$n = 20$$ free throws. What is the standard deviation of $$X$$, the number of successful free throws?

$$\sqrt{n p q} = \sqrt{20 \times 0.8 \times 0.2} = \sqrt{3.2} \approx 1.79$$

Q: The weights of newborn babies are approximately normally distributed with mean $$\mu = 7.4$$ pounds and standard deviation $$\sigma = 1.2$$ pounds. What weight corresponds to the 30th percentile?

$$x = \mu + z_{0.30} \sigma = 7.4 + (-0.524) \times 1.2 \approx 6.77$$ pounds

Q: Suppose $$A is $$the event that a person is widowed and $$B is $$the event that a person is female. Using the contingency table, are $$A$$ and $$B$$ independent?

No, because $$P(A \cap B) \neq P(A) \times P(B)$$

Question 1

A fair coin is flipped 3 times. What is the probability of getting exactly 2 heads?

Accepted Answer

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

Question 2

A hospital receives 8 blood pressure monitors, and 2 are defective. Two monitors are selected at random without replacement. What is the probability that both selected monitors are NOT defective?

Accepted Answer

$$\frac{15}{28}$$

Question 3

Given the following contingency table for marital status and gender in a community of 200 adults, what is the probability that a randomly selected person is widowed and female?

$$P(	ext{Widowed and Female}) = ?$$

Accepted Answer

$$\frac{15}{200}$$

Question 4

Given that a randomly selected person is female, what is the probability that she is widowed? Use the contingency table data.

Accepted Answer

$$\frac{15}{111}$$

Question 5

A club has 12 members. In how many ways can a president, vice president, and secretary be selected (no person holds more than one office)?

Accepted Answer

$$12 	imes 11 	imes 10 = 1320$$

Question 6

Which of the following is a continuous random variable?

Accepted Answer

The weight of a randomly selected watermelon

Question 7

Given the probability distribution for a random variable $$X$$:

$$
\begin{align*}
x & : -2 & 0 & 3 & 5 \
P(x) & : 0.25 & 0.40 & 0.20 & 0.15 \
\end{align*}
$$
What is the mean (expected value) of $$X$$?

Accepted Answer

$$0.85$$

Question 8

A student guesses on 8 true/false questions. Let $$X be $$the number of questions answered correctly. What is the probability that the student gets exactly 6 correct? (Assume $$p = 0.5$$ for a correct answer.)

Accepted Answer

$$\binom{8}{6} (0.5)^8$ = 28 	imes 0.00390625 = 0.109375$$

Question 9

A basketball player makes free throws with probability $$p = 0.80. $$Suppose the player attempts $$n = 20$$ free throws. What is the standard deviation of $$X$$, the number of successful free throws?

Accepted Answer

$$\sqrt{n p q} = \sqrt{20 	imes 0.8 	imes 0.2} = \sqrt{3.2} \approx 1.79$$

Question 10

SAT verbal scores are approximately normally distributed with mean $$\mu = 500$$ and standard deviation $$\sigma = 100. $$What is the probability that a student scores less than 620?

Accepted Answer

$$P(X \u003c 620) = P\left(Z \u003c \frac{620 - 500}{100}\right) = P(Z \u003c 1.2) \approx 0.8849$$

Question 11

The weights of newborn babies are approximately normally distributed with mean $$\mu = 7.4$$ pounds and standard deviation $$\sigma = 1.2$$ pounds. What weight corresponds to the 30th percentile?

Accepted Answer

$$x = \mu + z_{0.30} \sigma = 7.4 + (-0.524) 	imes 1.2 \approx 6.77$$ pounds

Question 12

A club has 12 members. In how many ways can a committee of 3 members be selected?

Accepted Answer

$$\binom{12}{3} = 220$$

Question 13

Which of the following variables is discrete?

Accepted Answer

The number of flat tires a driver gets in one year

Question 14

A student guesses on 8 true/false questions. What is the probability that the student gets fewer than 3 correct?

Accepted Answer

$$P(X \u003c 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0039 + 0.0313 + 0.1094 = 0.1446$$

Question 15

Suppose $$A is $$the event that a person is widowed and $$B is $$the event that a person is female. Using the contingency table, are $$A$$ and $$B$$ independent?

Accepted Answer

No, because $$P(A \cap B) 
eq P(A) 	imes P(B)$$

Question 16

A hospital receives 8 blood pressure monitors, and 2 are defective. Two monitors are selected at random without replacement. What is the probability that at least one defective monitor is selected?

Accepted Answer

$$1 - \frac{15}{28} = \frac{13}{28}$$

Question 17

SAT verbal scores are approximately normally distributed with mean $$\mu = 500$$ and standard deviation $$\sigma = 100. $$What is the probability that a student scores between 480 and 560?

Accepted Answer

$$P(480 \u003c X \u003c 560) = 0.3108$$

Question 18

A basketball player makes free throws with probability $$p = 0.80. $$Suppose the player attempts $$n = 20$$ free throws. What is the mean number of successful free throws?

Accepted Answer

$$n p = 20 	imes 0.8 = 16$$

Question 19

The weights of newborn babies are approximately normally distributed with mean $$\mu = 7.4$$ pounds and standard deviation $$\sigma = 1.2$$ pounds. What are the two weights that separate the middle 80% of baby weights from the lowest 10% and highest 10%?

Accepted Answer

$$7.4 \pm 1.28 	imes 1.2 = (5.86, 8.94)$$ pounds

STA2023 Practice Midterm 2 – Step-by-Step Statistics Guidance

Guida di studio - Domande di pratica

Study guide - Flashcard