The following data lists the number of correct and wrong dosage amounts calculated by 28 physicians. In a research experiment, a group of 14 physicians was given bottles of epinephrine labeled with a concentration of “1 milligram in 1 milliliter solution,” and another group of 14 physicians was given bottles labeled with a ratio of “1 milliliter of a 1:1000 solution.”
If one of the physicians is randomly selected, what is the probability of getting one who calculated the dose correctly?
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 96 people in the 18-21 age bracket and finds that 67 of them respond and 29 refuse to respond. When 252 people in the 22-29 age bracket are contacted, 213 respond and 39 refuse to respond. Suppose that one of the 348 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who responded.
The accompanying table contains the results from experiments with a polygraph instrument. Find the probabilities of the events in parts (a) and (b) below. Are these events unlikely?
a. Four of the test subjects are randomly selected with replacement, and they all had true negative test results.
b. Four of the test subjects are randomly selected without replacement, and they all had true negative test results.
The probability that all four test subjects had a true negative test result when they are randomly selected with replacement is 0.076
No, not unlikely because the probability of the event is greater than 0.05.
The probability that all four test subjects had a true negative test result when they are randomly selected without replacement is 0.072
No, not unlikely because the probability of the event is greater than 0.05.
A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with five different members. There are 13 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below.
a. How many different ways can the officers be appointed?
b. How many different ways can the committee be appointed?
c. What is the probability of randomly selecting the committee members and getting the five youngest of the qualified candidates?
In designing an experiment involving a treatment applied to 6 test subjects, researchers plan to use a simple random sample of 6 subjects selected from a pool of 28 available subjects. (Recall that with a simple random sample, all samples of the same size have the same chance of being selected.) Answer the questions below.
a. How many different simple random samples are possible?
b. What is the probability of each simple random sample in this case?
Consider a bag that contains 226 coins of which 4 are rare Indian pennies. For the given pair of events A and B, complete parts (a) and (b) below.
EVENT A: When one of the 226 coins is randomly selected, it is one of the 4 Indian pennies. EVENT B: When another one of the 226 coins is randomly selected (with replacement), it is also one of the 4 Indian pennies.
a. Determine whether events A and B are independent or dependent. b. Find P(A and B), the probability that events A and B both occur.
In a market research survey of 2869 motorists, 291 said that they made an obscene gesture in the previous month. Complete parts (a) and (b) below.
a. If 1 of the surveyed motorists is randomly selected, what is the probability that this motorist did not make an obscene gesture in the previous month?
b. If 50 of the surveyed motorists are randomly selected without replacement, what is the probability that none of them made an obscene gesture in the previous month? Should the 5% guideline be applied in this case?
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay.
A company has just manufactured 2000 CDs, and 611 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?
Does this outcome suggest that the entire batch consists of good CDs? Why or why not?
For the given pair of events A and B, complete parts (a) and (b) below.
EVENT A: When a page is randomly selected and ripped from a 2222-page document and destroyed, it is page 55.
EVENT B: When a different page is randomly selected and ripped from the document, it is page 99.
a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)
b. Find P(A and B), the probability that events A and B both occur.
