1 February 2012, 12:37 am
Question 1 A soft drink manufacturer claims that cans of soda contain , on average, 12 ounces. The machine that fills the cans actually delivers a variable amount of soda. The amount varies randomly according to a normal distribution with standard deviation 0.16 ounce. If you purchase a six-pack of sodas, and measure the amount in each can and find the average, the probability that the average of the six cans will be between 11.9 and 12.1 oz equals which standard normal probability? a.P(-.625 < Z < .625) b.P(-3.75 < Z < 3.75) c.P(-.1 < Z < .1) d.P(-1.53 < Z < 1.53) Question 2 National League Hockey play-off games go into overtime if the score is tied at the end of a game. Overtime lasts until one of the teams scores a goal. From years of experience we know that the distribution of the lengths of the overtime periods is right skewed with a mean of 9.8 minutes and a standard deviation of 12 minutes. What is the (approximate) probability that a random sample of 30 overtime periods would have a (sample) mean length of more than 13 minutes? Give your answer to 3 decimal places, e.g, 0.123. Question 3 The number of years of education of self-employed individuals in the U.S. has a population mean of 13.6 years and a population standard deviation of 3.0 years. If we survey a random sample of 100 self-employed people to determine the average number of years of education for the sample, what is the mean and standard deviation of the sampling distribution of x-bar(the sample mean)? Enter your answers below to one decimal place, e.g. 0.1. mean = years standard deviation = years Question 4 A bank that has an ATM machine on a college campus. They know the mean cash withdrawal for that machine is $22.50 and the standard deviation of withdrawals is $4.30. The bank will take a random sample of 40 transactions and compute the mean withdrawal for audit purposes. This sample size will produce a standard deviation for the sampling distribution of x-bar of $0.68. If the auditor wants to reduce that standard deviation by half (so as to have a more precise estimate of the mean), what sample size should she request that they use? a.80 b.160 c.20 d.1600 Question 5 The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not a normal distribution. Let "x-bar" be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate probability that "x-bar" is less than 2? a. 0.1515 b.0.5557 c.0.4443 d.0.8485 Question 6 The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not a normal distribution. Let "x-bar" be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate probability that there are fewer than 100 accidents in a year? (Hint: Restate this event in terms of "x-bar") a. 0.9236 b.0.0002 c..9998 d.0.0764 Question 7 Which of the following is a result of the Central Limit Theorem? A.The sampling distribution of the sample mean is always approximately normal. B.The sampling distribution of the sample mean looks more and more like the population distribution as the sample size increases. C.For sufficiently large samples, the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population distribution. D.Population distributions are approximately normal whenever the population is large.... Read More »
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