1. 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 nine 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_________
2. Sociologists say that 85% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that eight married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.)
(a) all of them dislike their mother-in-law_________
(b) none of them dislike their mother-in-law________
(c) at least six of them dislike their mother-in-law________
(d) no more than five of them dislike their mother-in-law_______
3. 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 15 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 13 ties are not too tight_________
4. The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of twelve syringes taken from the batch. Suppose the batch contains 1% defective syringes.
(a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, ..., 11 and 12 defective syringes in a random sample of twelve syringes.
(b) Find μ. (Enter your answer to two decimal places.)
μ = ________syringes
What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.)
_______ syringes
(c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.)
________
(d) Find σ. (Round your answer to three decimal places.)
σ = _________syringes
5. A company is in the business of finding addresses of long-lost friends. The company claims to have a 70% success rate. Suppose that you have the names of nine friends for whom you have no addresses and decide to use the company to track them.
(a) Make a histogram showing the probability of r = 0 to 9 friends for whom an address will be found.
(b) Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.)
μ = _______friends
σ = ________friends
What is the expected number of friends for whom addresses will be found? (Round your answer to the nearest whole number.)
_______friends
6. USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take eleven people at random off a city street.
(a) Make a histogram showing the probability distribution of the number of illiterate people out of the eleven people in the sample.
(b) Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.)
μ = _________people
σ = __________people
Find the expected number of people in this sample who are illiterate. (Round your answer to a whole number.)
________
7. Have you ever tried to get out of jury duty? About 25% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty†. If 15 people are called for jury duty, find the following.
(a) What is the probability that all 15 will be available to serve on the jury? (Round your answer to three decimal places.)
_________
(b) What is the probability that 9 or more will not be available to serve on the jury? (Round your answer to three decimal places.)
___________
(c) Find the expected number of those available to serve on the jury. What is the standard deviation? (Round your answers to two decimal places.)
μ = _______people
σ = _________people