Q: A club has 12 members. In how many ways can a president, vice president, and secretary be selected?

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

Q: A student guesses on 8 true/false questions. What is the probability that the student gets exactly 6 correct? (Let $$p = 0.5$$ for a correct guess.)

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

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

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

Q: Let $$A be $$the event that a person is widowed and $$B$$ the event that a person is female. Are $$A$$ and $$B$$ independent? (Use the marital status table.)

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

Q: A basketball player makes free throws with probability $$p = 0.80. If $$the player attempts $$n = 20$$ free throws, what is the mean number of successful free throws?

$$n \times p = 20 \times 0.8 = 16$$

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, 2 of which are defective. If 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 marital status table, what is the probability that a randomly selected person is 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 marital status table.)

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?

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

The random variable $$X$$ has the following probability distribution: $$x = -2, 0, 3, 5$$ with $$P(x) = 0.25, 0.40, 0.20, 0.15$$ respectively. What is the mean (expected value) of $$X$$?

Accepted Answer

$$0.65$$

Question 8

A student guesses on 8 true/false questions. What is the probability that the student gets exactly 6 correct? (Let $$p = 0.5$$ for a correct guess.)

Accepted Answer

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

Question 9

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

Accepted Answer

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

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

$$P(Z \u003c 1.2) \approx 0.8849$$

Question 11

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

Accepted Answer

$$7.4 + (z_{0.30})(1.2)$$, where $$z_{0.30} \approx -0.524$$; thus, $$7.4 + (-0.524)(1.2) \approx 6.77$$ 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

Let $$A be $$the event that a person is widowed and $$B$$ the event that a person is female. Are $$A$$ and $$B$$ independent? (Use the marital status table.)

Accepted Answer

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

Question 16

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

Accepted Answer

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

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

$$P(480 \u003c X \u003c 560) = P(-0.2 \u003c Z \u003c 0.6) = 0.7257 - 0.4207 = 0.3050$$

Question 18

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

Accepted Answer

$$1 - P(X \u003c 3) = 1 - 0.1446 = 0.8554$$

Question 19

The weights of newborn babies are 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

Find $$z_{0.10} \approx -1.28$$ and $$z_{0.90} \approx 1.28$$; thus, $$7.4 + (-1.28)(1.2) = 5.86$$ pounds and $$7.4 + (1.28)(1.2) = 8.94$$ pounds

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

Guida di studio - Domande di pratica

Study guide - Flashcard