1) A firm believes the internal rate of return for its proposedinvestment can be
ID: 2952357 • Letter: 1
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1) A firm believes the internal rate of return for its proposedinvestment can best be described by a normal distribution with mean32% and standard deviation 3%. What is theprobability that the internal rate of return for the investmentwill be at least 27.5%?
2) Farmers often sell fruits and vegetables at roadside standsduring the summer. One such roadside stand has a daily demand fortomatoes that is approximately normally distributed with a meanequal to 459 tomatoes per day and a standard deviation equal to 30tomatoes per day. If there are 417 tomatoes available to be sold atthe roadside stand at the beginning of a day, what is theprobability that they will all be sold?
3) The board of examiners that administers the real estate broker'sexamination in a certain state found that the mean score on thetest was 579 and the standard deviation was 72. If the board wantsto set the passing score so that only the best 10% of allapplicants pass, what is the passing score? Assume that the scoresare normally distributed.
4) The amount of time it takes a student to walk from her home toclass has a skewed right distribution with a mean of 12 minutes anda standard deviation of 2.3 minutes. If data were collected from 30randomly selected walks, describe the sampling distribution ofx,the sample mean time.
5) A survey of 500 non-fatal accidents showed that 222 involved theuse of a cell phone. Construct a 99% confidence interval for theproportion of fatal accidents that involved the use of a cellphone.
6) In a recent study of 95 eighth graders, the mean number of hoursper week that they watched television was 18.7. Assume standarddeviation = 5.5 hours.
a) Find the 95% confidence interval of the mean.
b) If the standard deviation is doubled to 11, what will be theeffect on the confidence interval?
7) In order to set rates, an insurance company is trying toestimate the number of sick days that full time workers at an autorepair shop take per year. A previous study indicated that thestandard deviation was 2.2 days.
a) How large a sample must be selected if the company wants to be90% confident that the true mean differs from the sample mean by nomore than 1 day?
b) Repeat part (a) using a 95% confidence interval. Whichlevel of confidence requires a larger sample size? Explain.
8) The principal at Lakewood Elementary would like to estimate themean length of time each day that it takes all the buses to arriveand unload the students. How large a sample is needed if theprincipal would like to assert with 90% confidence that the samplemean is off by, at most, 7 minutes. Assume standard deviation = 14minutes.
9) In a college student poll, it is of interest to estimate theproportion p of students in favor of changing from a quarter-systemto a semester-system. How many students should be polled so that wecan estimate p to within .09 using a 99% confidence interval?
10) In a survey of 10 golfers, 2 were found to be left-handed. Isit practical to construct the 90% confidence interval for thepopulation proportion, p? Explain.
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