Question 1

Which of the following is a discrete random variable?

Accepted Answer

The number of gold balls in a golf bag

Question 2

Which of the following is NOT a requirement for a probability distribution?

Accepted Answer

All probabilities must be negative.

Question 3

Given the probability distribution below, determine if it is valid. If not, state the violated requirement.

$$\begin{array}{c|c}
X & P(X) \
\hline
0 & 0.2 \
1 & 0.3 \
2 & 0.4 \
3 & 0.2 \
\end{array}$$

Accepted Answer

Invalid: The sum of probabilities is greater than 1

Question 4

Find the mean of the following probability distribution:

$$\begin{array}{c|c}
X & P(X) \
\hline
1 & 0.1 \
2 & 0.3 \
3 & 0.4 \
4 & 0.2 \
\end{array}$$

Use $$\mu = \sum [x \cdot P(x)].$$

Accepted Answer

$$2.7$$

Question 5

A binomial experiment consists of 10 trials with a probability of success $$p = 0.3. $$What is the probability of exactly 4 successes? Use the binomial probability formula:

$$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$

Accepted Answer

$$0.2001$$

Question 6

Which of the following scenarios results in a binomial distribution?

Accepted Answer

Surveying 20 people to see if they prefer tea or coffee

Question 7

Find the standard deviation for a binomial distribution with $$n = 12$$ and $$p = 0.4. $$Use $$\sigma = \sqrt{np(1-p)}.$$

Accepted Answer

$$1.697$$

Question 8

A person has a 0.15 probability of being immune to a particular disease. What is the expected number of immune people in a random sample of 40?

Accepted Answer

$$6$$

Question 9

Given a normal distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what is the minimum usual value? Use $$\mu - 2\sigma.$$

Accepted Answer

$$70$$

Question 10

A researcher randomly selects 10 newborn babies and counts the number of girls. What is the probability of selecting exactly 4 girls? Assume $$p = 0.5$$ for a girl. Use the binomial formula.

Accepted Answer

$$0.205$$

Question 11

Which of the following is a continuous random variable?

Accepted Answer

The time it takes to commute to work

Question 12

A probability distribution is given by $$P(X) = \{-0.1, 0.3, 0.4, 0.4\}. Is $$this a valid probability distribution?

Accepted Answer

No, because one probability is negative

Question 13

If a binomial distribution has $$n = 8$$ and $$p = 0.25$$, what is the mean number of successes? Use $$\mu = np.$$

Accepted Answer

$$2$$

Question 14

A company tests 5 products and finds that each has a 0.8 probability of passing quality control. What is the probability that exactly 3 products pass?

Accepted Answer

$$0.2048$$

Question 15

Which of the following best describes the expected value in a probability distribution?

Accepted Answer

The average value weighted by probability

Question 16

A probability distribution for the number of heads in 3 coin tosses is given by $$P(X=0)=0.125$$, $$P(X=1)=0.375$$, $$P(X=2)=0.375$$, $$P(X=3)=0.125. $$What is the mean number of heads?

Accepted Answer

$$1.5$$

Question 17

If a random variable $$X$$ has the following probability distribution: $$P(X=1)=0.2$$, $$P(X=2)=0.5$$, $$P(X=3)=0.3$$, what is the variance? Use $$\$$sigma^2$$ = \sum [x^2$ \cdot P(x)] - \mu^2$.

Accepted Answer

$$0.46$$

Question 18

A student scores 1, 2, 3, and 4 on four quizzes. If each score is equally likely, what is the expected score?

Accepted Answer

$$2.5$$

Question 19

Which of the following is NOT a characteristic of a binomial experiment?

Accepted Answer

Probability of success changes from trial to trial

Discrete Probability Distributions and Binomial Distributions: Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드