Q: If $$n = 30$$ and $$p = 0.56$$, what is the mean number of cloudy days in June in Pittsburgh?

$$\mu = np = 30 \times 0.56 = 16.8$$

Q: A binomial experiment has $$n = 5$$ and $$p = 0.2. $$What is the standard deviation?

$$\sigma = \sqrt{npq} = \sqrt{5 \times 0.2 \times 0.8} \approx 0.894$$

Question 1

Which of the following is NOT a requirement for a probability experiment to be classified as a binomial experiment?

Accepted Answer

The probability of success must change from trial to trial.

Question 2

A pharmaceutical company tests a new drug on 10 patients. Each patient has a 70% chance of experiencing a positive effect. What is the probability that exactly 7 patients experience a positive effect? Use the binomial probability formula.

Accepted Answer

$$P(7) = \frac{10!}{7!3!} (0.7)^7$ (0.3)^3$

Question 3

Which scenario below is NOT a binomial experiment?

Accepted Answer

Drawing 3 cards from a deck without replacement and counting the number of aces.

Question 4

Given $$n = 8$$, $$p = 0.05$$, and $$x = 3$$, what is the probability that exactly 3 out of 8 workers commute by public transportation? (Use the binomial probability formula.)

Accepted Answer

$$P(3) = \frac{8!}{3!5!} (0.05)^3$ (0.95)^5$

Question 5

A survey found that 22% of U.S. adults say the economy is the most important problem. If you randomly select 4 adults, what is the probability that at least 2 respond yes?

Accepted Answer

$$P(x \geq 2) = P(2) + P(3) + P(4)$$

Question 6

If $$n = 30$$ and $$p = 0.56$$, what is the mean number of cloudy days in June in Pittsburgh?

Accepted Answer

$$\mu = np = 30 	imes 0.56 = 16.8$$

Question 7

Which formula correctly gives the variance of a binomial distribution?

Accepted Answer

$$\$$sigma^2$$ = npq$$

Question 8

A doctor performs a surgery with a 90% success rate on 3 patients. What is the probability that exactly 2 surgeries are successful?

Accepted Answer

$$P(2) = \frac{3!}{2!1!} (0.9)^2$ (0.1)^1$ = 0.243$$

Question 9

If $$n = 100$$, $$p = 0.75$$, and $$x = 66$$, which technology command would you use on a TI-84 calculator to find $$P(x = 66)$$?

Accepted Answer

binompdf(100, 0.75, 66)

Question 10

Which of the following best describes the random variable $$X in a $$binomial experiment?

Accepted Answer

$$X is $$the number of successes in $$n$$ trials.

Question 11

A binomial experiment has $$n = 5$$ and $$p = 0.2. $$What is the standard deviation?

Accepted Answer

$$\sigma = \sqrt{npq} = \sqrt{5 	imes 0.2 	imes 0.8} \approx 0.894$$

Question 12

Which of the following is a real-world example of a binomial experiment?

Accepted Answer

Counting the number of defective products in a batch of 50, where each product is tested independently.

Question 13

If the probability of success in a single trial is $$p$$, what is the probability of failure?

Accepted Answer

$$q = 1 - p$$

Question 14

A survey asks 6 adults if they go online several times a day. If 48% say yes, what is the probability that exactly 3 say yes?

Accepted Answer

$$P(3) = \frac{6!}{3!3!} (0.48)^3$ (0.52)^3$

Question 15

Which of the following statements is TRUE about the sum of all probabilities in a binomial probability distribution?

Accepted Answer

The sum is always 1.

Binomial Probability Distributions: Concepts, Calculations, and Applications

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