Q: If $$n = 30$$, $$p = 0.33$$, and $$q = 0.67$$, what is the mean number of days with precipitation in June?

$$\mu = np = 30 \times 0.33 = 9.9$$

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, independent of the others. What is the probability that exactly 7 patients experience a positive effect? Use the binomial probability formula.

Accepted Answer

$$P(X = 7) = \binom{10}{7} (0.7)^7$ (0.3)^3$

Question 3

Which of the following scenarios is NOT a binomial experiment?

Accepted Answer

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

Question 4

Given a binomial distribution with $$n = 8$$ and $$p = 0.15$$, what is the probability that exactly 5 successes occur? (Use the binomial probability formula.)

Accepted Answer

$$P(X = 5) = \binom{8}{5} (0.15)^5$ (0.85)^3$

Question 5

A survey found that 62% of adults say inflation is a very big problem. If you randomly select 4 adults, what is the probability that at least 2 of them say inflation is a very big problem?

Accepted Answer

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

Question 6

If $$n = 30$$, $$p = 0.33$$, and $$q = 0.67$$, what is the mean number of days with precipitation in June?

Accepted Answer

$$\mu = np = 30 	imes 0.33 = 9.9$$

Question 7

Which formula gives the variance of a binomial distribution?

Accepted Answer

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

Question 8

A doctor performs a surgery with an 85% success rate on 8 patients. What are the possible values for the random variable $$x$$, the number of successful surgeries?

Accepted Answer

$$x = 0, 1, 2, 3, 4, 5, 6, 7, 8$$

Question 9

If the probability of an event is less than 0.05, how is the event typically classified?

Accepted Answer

Unusual

Question 10

A survey found that 38% of adults struggle to limit screen time. If you randomly select 100 adults, what is the probability that exactly 29 struggle to limit their screen time? (Use technology or the binomial formula.)

Accepted Answer

Approximately 0.015

Question 11

Which of the following best describes the standard deviation of a binomial distribution?

Accepted Answer

$$\sigma = \sqrt{npq}$$

Question 12

In a binomial experiment with $$n = 6$$ and $$p = 0.42$$, what is the probability that none of the 6 adults respond 'not at all closely' to following sports?

Accepted Answer

$$P(X = 0) = (0.58)^6$

Question 13

A jar contains 5 red, 9 blue, and 6 green marbles. You select 3 marbles without replacement and count the number of red marbles. Why is this NOT a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial.

Question 14

If the mean number of days with precipitation in June is 9.9 and the standard deviation is about 2.6, which of the following would be considered an unusual value?

Accepted Answer

A June with 16 or more days of precipitation

Question 15

Which of the following is the correct formula for the probability of exactly $$x$$ successes in $$n$$ binomial trials?

Accepted Answer

$$P(X = x) = \binom{n}{x} p^x q$$^{n-x}$$

Discrete Probability Distributions: Binomial Distributions

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