Exam 22: Binomial Distribution and Normal Approximation

SCENARIO 6-7 A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15. -Referring to Scenario 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be less than 8 computers that require repair on a given day using a normal approximation.

SCENARIO 9-12 A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic. -Referring to Scenario 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.01,the probability of the company not marketing the new local anesthetic when its population mean effective time is not greater than the 7.4 minutes is .

SCENARIO 7-8 According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor. -Referring to Scenario 7-8,the mean of all the sample proportions of 50 customers who will make a purchase after visiting the web site is .

SCENARIO 16-16 Given below are the prices of a basket of four food items from 2008 to 2012. -Referring to Scenario 16-16,what are the simple price indices for wheat,corn,soybeans and milk,respectively,in 2010 using 2012 as the base year?

SCENARIO 16-15 Given below are the average prices for three types of energy products for five consecutive years. -Referring to Scenario 16-15,what are the simple price indices for electricity,natural gas and fuel oil,respectively,in year 3 using year 1 as the base year?

To determine the probability of getting fewer than 3 events of interest in a binomial distribution,you will find the area under the normal curve for X = 3.5 and below.

SCENARIO 12-19 The director of the MBA program of a state university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good.Given below is the result from 215 students' view of the program before and after the orientation. -Referring to Scenario 12-19,which test should she use?

SCENARIO 16-16 Given below are the prices of a basket of four food items from 2008 to 2012. -Referring to Scenario 16-16,what are the simple price indices for wheat,corn,soybeans and milk,respectively,in 2011 using 2008 as the base year?

SCENARIO 9-11 An appliance manufacturer claims to have developed a compact microwave oven that consumes a population mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim. -Referring to Scenario 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.10,the probability of making a Type II error is _____ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

SCENARIO 9-11 An appliance manufacturer claims to have developed a compact microwave oven that consumes a population mean of no more than 250 W.From previous studies,it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim. -Referring to Scenario 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.05,the probability of making a Type II error is _____ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

Which of the below listed options is(are)true?

SCENARIO 12-20 A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Scenario 12-20,which is the appropriate test to use?

Statistical significance can eventually be found when the sample size becomes large enough.

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because a random variable having a binomial distribution can have only a specified value while a random variable having a normal distribution can take on any values within an interval around that specified value.

SCENARIO 8-12 The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year.A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year. -Referring to Scenario 8-12,the superintendent can conclude with 95% level of confidence that no more than 5% of the students in the unified school district skipped more than 10 days of school last year.

SCENARIO 12-20 A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Scenario 12-20,what is the value of the test statistic?

The Paasche price index reflects more accurately the consumption cost at a point in time because it uses the consumption quantities in the initial year as the base.

SCENARIO 8-13 The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months. -Referring to Scenario 8-13,using the 90% one-sided confidence interval,the president can be 95% confident that no more than 5% of the students at the university had used illicit drugs during the last 12 months.

The Laspeyres price index uses the initial consumption quantities as the weights.

To construct a bootstrap confidence interval estimate for the population mean,you will order the resampled means for the m samples that you have drawn from the initial sample of size n,use the value of the resampled mean that cuts off the smallest $\alpha$ / 2 $\alpha$ 100% as the lower limit and the value of that cuts off the largest $\alpha$ / 2 $\alpha$ 100% as the upper limit.