statistics
dr.two
Question
- Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on alleight questions, find the indicated probabilities. (Round your answers to three decimal places.)(a) What is the probability that he will answer all questions correctly?
(b) What is the probability that he will answer all questions incorrectly?
(c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table.
Then use the fact that P(r ? 1) = 1 ? P(r = 0).
Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference?
(d) What is the probability that Richard will answer at least half the questions correctly? - The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 5% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of seven adult friends, what is the probability of the following? (Round your answers to three decimal places.)(a) no one has done a one-time fling
(b) at least one person has done a one-time fling
(c) no more than two people have done a one-time fling - A research team conducted a study showing that approximately 25% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)(a) at least one tie is too tight
(b) more than two ties are too tight
(c) no tie is too tight
(d) at least 18 ties are not too tight - Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 65% of the business days it is open. Estimate the probability that the store will gross over $850 for the following. (Round your answers to three decimal places.)(a) at least 3 out of 5 business days
(b) at least 6 out of 10 business days
(c) fewer than 5 out of 10 business days
(d) fewer than 6 out of the next 20 business days
If the outcome described in part (d) actually occurred, might it shake your confidence in the statement p = 0.65? Might it make you suspect that p is less than 0.65? Explain.
(e) more than 17 out of the next 20 business days
If the outcome described in part (e) actually occurred, might you suspect that p is greater than 0.65? Explain. - Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey, 47% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability of the following.(a) Out of six adults, none is concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)
(b) Out of six adults, all are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.)
(c) Out of six adults, exactly four are concerned that employers are monitoring phone calls. (Round your answer to three decimal places.) - Study the binomial distribution table. Notice that the probability of success on a single trial p ranges from 0.01 to 0.95. Some binomial distribution tables stop at 0.50 because of the symmetry in the table. Let's look for that symmetry. Consider the section of the table for which n = 5. Look at the numbers in the columns headed by p = 0.30 and p = 0.70. Do you detect any similarities? Consider the following probabilities for a binomial experiment with five trials.(a) Compare P(3 successes), where p = 0.30, with P(2 successes), where p = 0.70.
(b) Compare P(3 or more successes), where p = 0.30, with P(2 or fewer successes), where p = 0.70.
(c) Find the value of P(4 successes), where p = 0.30. (Round your answer to three decimal places.)
P(4 successes) =
For what value of r is P(r successes) the same using p = 0.70?
r =
(d) What column is symmetrical with the one headed by p = 0.20?
Details
Purchase An Answer Below
