Question 1

One application of the binomial distribution formula or one number in Table V (in your textbook) is always the answer to what kind of question?
A) exactly
B) at most
C) at least
D) between

Accepted Answer

The binomial distribution formula or Table V is directly used to find the probability of an event happening "exactly" a certain number of times in a fixed number of trials.

Question 2

To calculate the probability of obtaining three aces in eight draws of a card with replacement from an ordinary deck, we would use the
A) hypergeometric distribution.
B) Poisson distribution.
C) binomial distribution.
D) multinomial distribution.

Accepted Answer

The binomial distribution is used for calculating the probability of obtaining a specific number of successes (in this case, drawing an ace) in a fixed number of independent trials (eight draws), with replacement, where each trial has only two possible outcomes (success or failure).

Question 3

To calculate the probability of obtaining three aces in eight draws of a card without replacement, the required distribution is the
A) hypergeometric distribution.
B) Poisson distribution.
C) binomial distribution.
D) multinomial distribution.

Accepted Answer

The hypergeometric distribution is used when we are dealing with successes and failures in a sample drawn without replacement from a finite population, which exactly describes the scenario of drawing aces from a deck of cards.

Question 4

If a binomial distribution problem has $\mathrm{p}=0.003$ and $\mathrm{n}=1000$, then the answer should be approximated by using
A) Table V (in your textbook).
B) the Poisson distribution.
C) the hypergeometric distribution.
D) the multinomial distribution.

Accepted Answer

When the probability of success ($p$) is very small and the number of trials ($n$) is large, the binomial distribution can be approximated by the Poisson distribution. This is especially true when $np$ is less than or equal to 10, which is the case here ($0.003 \times 1000 = 3$).

Question 5

One application of the Poisson distribution formula is always the answer to what kind of question?
A) exactly
B) at most
C) at least
D) between

Accepted Answer

The Poisson distribution formula is specifically used to find the probability of a given number of events happening in a fixed interval of time or space, hence it answers questions related to the probability of an event happening "exactly" a certain number of times.

Question 6

A die is rolled 10 times. The probability of obtaining from 4 to 7 threes should be determined using the formula for the
A) hypergeometric distribution.
B) Poisson distribution.
C) binomial distribution.
D) multinomial distribution.

Accepted Answer

The binomial distribution is used to model the number of successes in a fixed number of independent Bernoulli trials, with a constant probability of success. Rolling a die and counting the number of threes fits this scenario, where each roll is independent, and the probability of getting a three is constant (1/6).

Question 7

A service station receives an average of six customers per hour. The probability that there will be three arrivals in a given hour can be found by using the
A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) multinomial distribution.

Accepted Answer

The Poisson distribution is used to model the number of events in fixed intervals of time or space when these events occur with a known constant mean rate and independently of the time since the last event. In this case, it is used to find the probability of a specific number of arrivals (customers) at a service station in a given hour, given a known average rate of arrivals.

Question 8

A multiple choice test consists of seven questions with five choices each. If a student guesses on all questions the probability that a student gets exactly 3 correct answers is given by
A) $\left(\begin{array}{l}7 \ 3\end{array}\right)\left(\frac{3}{5}\right)^{3}\left(\frac{2}{5}\right)^{4}$
B) $\left(\begin{array}{l}7 \ 5\end{array}\right)\left(\frac{1}{3}\right)^{5}\left(\frac{2}{3}\right)^{2}$
C) $\left(\begin{array}{l}7 \ 5\end{array}\right)\left(\frac{1}{5}\right)^{3}\left(\frac{4}{5}\right)^{4}$
D) $\left(\begin{array}{l}7 \ 3\end{array}\right)\left(\frac{1}{5}\right)^{3}\left(\frac{4}{5}\right)^{4}$

Accepted Answer

The correct formula for calculating the probability of getting exactly 3 correct answers out of 7 questions, when each question has 5 choices, is given by the combination of choosing 3 correct answers out of 7 ($7C3$) times the probability of getting those 3 answers right ($\left(\frac{1}{5}\right)^3$) and the remaining 4 wrong ($\left(\frac{4}{5}\right)^4$).

Question 9

We want to determine the probability of obtaining at most 4 successful operations in 10 independent surgical operations where the probability of success is the same for each operation. The appropriate formula to be used is
A) the binomial formula.
B) the mean of the binomial distribution.
C) the hypergeometric formula.
D) the mean of the hypergeometric distribution.

Accepted Answer

The binomial formula is appropriate for calculating the probability of a certain number of successes in a fixed number of independent trials, each with the same probability of success, which matches the scenario described.

Question 10

Which of the following formulas, when applicable, gives exact answers to probability questions involving the binomial distribution?
A) the binomial formula
B) Table V
C) the hypergeometric formula
D) the Poisson formula

Accepted Answer

The binomial formula is specifically designed for calculating probabilities in binomial distribution scenarios, where there are a fixed number of independent trials, each with two possible outcomes.

Question 11

Which of the following can be probability distributions? Justify your answer.
a. $f(1)=0.40, f(2)=0.20, f(3)=0.50$ where the random variable can take on only the values 1,2 , and 3 .
b. $f(x)=x / 10$ for $x=0,1,2,3,4$.
c. $f(1)=0.25, f(2)=0.30, f(3)=0.15, f(4)=0.15$ where the random variable can take on only the values $1,2,3$ and 4 .
d. $f(x)=\frac{x-3}{7}$ for $x=0,1,2,3,4,5$

Accepted Answer

The answer of Which of the following can be probability...

Question 12

Experience has shown that $20 \%$ of a certain airline's flights leaving Green Field airport have to be delayed due to weather conditions. Determine the probability that among twenty flights at Green Field airport at most three will have to be delayed due to weather conditions. Round to the nearest thousandth.

Accepted Answer

The answer of Experience has shown that $20 \%$ of...

Question 13

A study shows that $90 \%$ of the tomatoes shipped out by a large tomato grower are ripe and ready to eat. Find the probability that among 50 tomatoes shipped out by this grower all are ripe and ready to eat. Round to the nearest thousandth.

Accepted Answer

The answer of A study shows that $90 \%$ of...

Question 14

Check whether the condition for the binomial approximation to the hypergeometric distribution is satisfied if a $=150, \mathrm{~b}=270$, and $\mathrm{n}=21$.

Accepted Answer

The answer of Check whether the condition for the binomial...

Question 15

Check whether the condition for the binomial approximation to the hypergeometric distribution is satisfied if a $=230, \mathrm{~b}=290$, and $\mathrm{n}=27$.

Accepted Answer

The answer of Check whether the condition for the binomial...

Question 16

Among 18 job applicants, six are actually qualified to do the job. Assume seven applicants are randomly selected to be hired.}
-Find the probability that in this sample from two to four applicants are qualified.

Accepted Answer