Chapter 5.2 Homework

1.   Based on a​ survey, assume that 47​% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly​ selected, exactly two of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

The value of n is ____  (Type an integer or a decimal. Do not​ round.)

The value of x is ______  (Type an integer or a decimal. Do not​ round.)

The value of p is  _____  (Type an integer or a decimal. Do not​ round.)

The value of q is ______  (Type an integer or a decimal. Do not​ round.)

2.   Multiple-choice questions each have four possible answers (a, b, c, d)​, one of which is correct. Assume that you guess the answers to three such questions.

Use the multiplication rule to find ​P(WWC​), where C denotes a correct answer and W denotes a wrong answer. _____ ​(Type an exact​ answer.)

Beginning with WWC​, make a complete list of the different possible arrangements of one correct answer and two wrong answers​, then find the probability for each entry in the list. ​P(WWC​)−see above

Based on the preceding​ results, what is the probability of getting exactly one correct answer when three guesses are​ made? _______ (Type an exact​ answer.)

3.   Assume that random guesses are made for seven multiple choice questions on an SAT​ test, so that there are n=7 ​trials, each with probability of success​ (correct) given by p=0.4.

Find the indicated probability for the number of correct answers.

Find the probability that the number x of correct answers is fewer than 4.

4.   Assume that random guesses are made for 2 ​multiple-choice questions on a test with 2 choices for each​ question, so that there are n=2 ​trials, each with probability of success​ (correct) given by p=0.50.  Find the probability of no correct answers.

The probability of no correct answers is  ______

5.  Assume that when adults with smartphones are randomly​ selected, 53​% use them in meetings or classes. If 5 adult smartphone users are randomly​ selected, find the probability that exactly 2 of them use their smartphones in meetings or classes.

The probability is ______

6.  Assume that when adults with smartphones are randomly​ selected, 59​% use them in meetings or classes. If 20 adult smartphone users are randomly​ selected, find the probability that exactly 14 of them use their smartphones in meetings or classes.

The probability is ______  (Round to four decimal places as​ needed.)

7.  Assume that when adults with smartphones are randomly​ selected, 46​% use them in meetings or classes. If 8 adult smartphone users are randomly​ selected, find the probability that at least 6 of them use their smartphones in meetings or classes.

The probability is ______

8.   Assume that when adults with smartphones are randomly​ selected, 55​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that fewer than 4 of them use their smartphones in meetings or classes.

The probability is ______.   (Type an integer or decimal rounded to four decimal places as​ needed.)

9.  Based on a​ poll, 40​% of adults believe in reincarnation. Assume that 8 adults are randomly​ selected, and find the indicated probability. Complete parts​ (a) through​ (d) below.

What is the probability that exactly 7 of the selected adults believe in​ reincarnation?

The probability that exactly 7 of the 8 adults believe in reincarnation is _____  (Round to three decimal places as​ needed.)

What is the probability that all of the selected adults believe in​ reincarnation?

The probability that all of the selected adults believe in reincarnation is _______ ​(Round to three decimal places as​ needed.)

What is the probability that at least 7 of the selected adults believe in​ reincarnation?

The probability that at least 7 of the selected adults believe in reincarnation is ______  (Round to three decimal places as​ needed.)

If 8 adults are randomly​ selected, is 7 a significantly high number who believe in​ reincarnation?

1. No​, because the probability that 7 or more of the selected adults believe in reincarnation is greater than 0.05.
2. No​, because the probability that 7 or more of the selected adults believe in reincarnation is less than 0.05.
3. Yes​, because the probability that 7 or more of the selected adults believe in reincarnation isgreater than 0.05.
4. Yes​, because the probability that 7 or more of the selected adults believe in reincarnation is lessthan 0.05.

10.  Based on a​ poll, among adults who regret getting​ tattoos, 16​% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly​ selected, and find the indicated probability. Complete parts​ (a) through​ (d) below.

Find the probability that none of the selected adults say that they were too young to get tattoos. ____​(Round to four decimal places as​ needed.)

Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos. _____ ​(Round to four decimal places as​ needed.)

Find the probability that the number of selected adults saying they were too young is 0 or 1. _____ (Round to four decimal places as​ needed.)

If we randomly select five ​adults, is 1 a significantly low number who say that they were too young to get​ tattoos?  _______ because the probability that _________ of the selected adults say that they were too young is ___________0.05.

11.  The probability of a randomly selected adult in one country being infected with a certain virus is 0.004. In tests for the​ virus, blood samples from 17 people are combined. What is the probability that the combined sample tests positive for the​ virus? Is it unlikely for such a combined sample to test​ positive? Note that the combined sample tests positive if at least one person has the virus.

The probability that the combined sample will test positive is ______  ​(Round to three decimal places as​ needed.)

Is it unlikely for such a combined sample to test​ positive?

1. It is unlikely for such a combined sample to test​ positive, because the probability that the combined sample will test positive is less than or equal to 0.05.
2. It is not unlikely for such a combined sample to test​ positive, because the probability that the combined sample will test positive is less than or equal to 0.05.
3. It is unlikely for such a combined sample to test​ positive, because the probability that the combined sample will test positive is greater than 0.05.
4. It is not unlikely for such a combined sample to test​ positive, because the probability that the combined sample will test positive is greater than 0.05.

12.  A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 56 ​tablets, then accept the whole batch if there is only one or none that​ doesn’t meet the required specifications. If one shipment of 7000 aspirin tablets actually has a 5​% rate of​ defects, what is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?

The probability that this whole shipment will be accepted is ______   (Round to four decimal places as​ needed.)

The company will accept  _______ of the shipments and will reject _____ of the​ shipments, so  _______  (Round to two decimal places as​ needed.)

13.   When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 47 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 3000 ​batteries, and 2​% of them do not meet specifications. What is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?

The probability that this whole shipment will be accepted is ______  (Round to four decimal places as​ needed.)

The company will accept _____ of the shipments and will reject ______ of the​ shipments, so ________  (Round to two decimal places as​ needed.)

14.    Which of the following is not a requirement of the binomial probability​ distribution?  Choose the correct answer below.

1. The probability of a success remains the same in all trials.
2. The procedure has a fixed number of trials.
3. The trials must be dependent.
4. Each trial must have all outcomes classified into two categories

15 . Fill in the blank.  In the binomial probability​ formula, the variable x represents the​ _______.

16.  Which of the following is NOT one of the three methods for finding binomial probabilities that is found in the chapter on discrete probability​ distributions? Choose the correct answer below.

1. Use computer software or a calculator
2. Use a statistical table for binomial probabilities
3. Use a simulation
4. Use the binomial probability formula

17.   For the binomial​ distribution, which formula finds the standard​ deviation? Choose the correct answer below.

1. $\sqrt{npq}$
2. np
3. $\sqrt{np}$
4. npq