# DAT 565 Practice Week 3 Exercise

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1. Which of the following is a continuous random variable?

a. Number of Honda Civics sold in a given day at a car dealership.

b. Amount of gasoline used for a 200-mile trip in a Honda Civic.

c. Distance driven on a particular Thursday by the owner of a Honda Civic.

1. The probability is 1 in 4,007,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 48,000 trips.

(a) What is the probability of a fatal accident over a lifetime?

(b) Why might the assumption of independence be violated?

(c) Why might a driver be tempted not to use a seat belt "just on this trip"?

1. (a) A poll of 2,224 likely voters was conducted on the president’s performance. Approximately what margin of error would the approval rating estimate have if the confidence level is 95%?

(b) The poll showed that 48 percent approved the president’s performance. Construct a 90 percent confidence interval for the true proportion. (Round your answers to 4 decimal places.)

(c) Would you agree that the percentage of all voters opposed is likely to be 50 percent?

1. The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. All observations were below the allowable maximum, as shown by the reported range of contaminant levels. (presumably the mean would be the midrange).

1. A web server hosting company advertises 99.999 percent guaranteed network uptime.

(a) How many independent network servers would be needed if each has 97 percent reliability?

(b) How many independent network servers would be needed if each has 88 percent reliability?

1. A random sample of 30 lunch orders at Noodles & Company showed a standard deviation of \$5.31. Find the 90 percent confidence interval for the population standard deviation. Use Excel to obtain χ2L=CHISQ.INV(α/2,d.f.)χL2=CHISQ.INV(α/2,d.f.) and χ2U=CHISQ.INV.RT(α/2,d.f.)χU2=CHISQ.INV.RT(α/2,d.f.)

1. Jim's systolic blood pressure is a random variable with a mean of 145 mmHg and a standard deviation of 20 mmHg. For Jim's age group, 140 is the threshold for high blood pressure.

(a) If Jim's systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 135 or less?

(b) If Jim's systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 175 or more?

(c) If Jim's systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be between 125 and 165?

1. The time it takes to give a man a shampoo and haircut is normally distributed with mean 22 minutes and standard deviation 3 minutes. Customers are scheduled every 30 minutes.

(a) What is the probability that a male customer will take longer than the allotted time?

(b) If three male customers are scheduled sequentially on the half-hour, what is the probability that all three will be finished within their allotted half-hour times? (Round your answer to 4 decimal places.)

1. Which pairs of events are independent?

(a) P(J) = .10, P(K) = .80, P(J ∩ K) = .60.

(b) P(J) = .50, P(K) = .60, P(J ∩ K) = .30.

(c) P(J) = .15, P(K) = .30, P(J ∩ K) = .10.

1. If the weight (in grams) of cereal in a box of Lucky Charms is N(484,8), what is the probability that the box will contain less than the advertised weight of 456 g? Note: You may need to use Excel to calculate the exact probabilities. (Round your answer to 5 decimal places.)

1. In CABG surgery, there is a .00014 probability of a retained foreign body (e.g., a sponge or a surgical instrument) left inside the patient.

(a) In 100,000 CABG surgeries, what is the expected number of retained foreign bodies?

(b) What is the Poisson approximation to the binomial probability of five or fewer retained foreign bodies in 100,000 CABG surgeries? (Round your answer to 4 decimal places.)

1. Noodles & Company wants to estimate the percent of customers who order dessert, with 95% confidence and an error of ±10%. What is the required sample size? (Round up your answer to the next whole number.)

1. (a) Calculate the probabilities given below: (Round your answers to 4 decimal places.)

(b) Do you see evidence that smoking and race are not independent?

(c) Why might public health officials be interested in this type of data?

1. Prior to the start of the 2016 NCAA Men’s Basketball playoffs, the reported odds that Butler University would not make it to the final game were 123 to 1.What was the implied probability that Butler would make it to the finals in 2016?

1. The probability that a 2011 Audi A8 will be stolen is .0048.

Find the odds against the theft of a 2011 Audi A8. Round your answer to the nearest whole number.

1. In a certain microwave oven on the high power setting, the time it takes a randomly chosen kernel of popcorn to pop is normally distributed with a mean of 140 seconds and a standard deviation of 25 seconds.

(a) What percentage of the kernels will fail to pop if the popcorn is cooked for 2 minutes?

(b) What percentage of the kernels will fail to pop if the popcorn is cooked for 3 minutes?

(c) If you wanted 95 percent of the kernels to pop, what time would you allow?

(d) If you wanted 99 percent of the kernels to pop, what time would you allow?

1. Suppose the probability of an IRS audit is 5.2 percent for U.S. taxpayers who file form 1040 and who earned \$100,000 or more.

(a) What are the odds that such a taxpayer will be audited?

(b) What are the odds against such a taxpayer being audited?

1. Car security alarms go off at a mean rate of 3.8 per hour in a large Costco parking lot.

Find the probability that in an hour there will be

1. The probability that a student has a Visa card (event V) is .78. The probability that a student has a MasterCard (event M) is .17. The probability that a student has both cards is .09.

(a) Find the probability that a student has either a Visa card or a MasterCard.

(b) In this problem, are V and M independent?

1. If the weight (in grams) of cereal in a box of Lucky Charms is N(471,5), what is the probability that the box will contain less than the advertised weight of 459 g? Note: You may need to use Excel to calculate the exact probabilities.

1. A random sample of 27 lunch orders at Noodles & Company showed a mean bill of \$10.50 with a standard deviation of \$4.57. Find the 98 percent confidence interval for the mean bill of all lunch orders.
2. The probability that a 30-year-old white male will live another year is .99863.What premium would an insurance company charge to break even on a one-year, \$1 million term life insurance policy?

1. Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86.

(a) Construct a 90% confidence interval for the proportion of all kernels that would not pop.

(b) Is the normality assumption valid?

24)       A survey of 141 introductory statistics students showed the following contingency table.

25)       The probability of being struck by lightning is 0.00016.

Find the odds against being struck by lightning.

26)       In CABG surgery, there is a .00014 probability of a retained foreign body (e.g., a sponge or a surgical instrument) left inside the patient.

(a) In 100,000 CABG surgeries, what is the expected number of retained foreign bodies?

(b) What is the Poisson approximation to the binomial probability of five or fewer retained foreign bodies in 100,000 CABG surgeries? (Round your answer to 4 decimal places.)

27)       The probability that an international flight leaving the United States is delayed in departing (event D) is .23. The probability that an international flight leaving the United States is a transpacific flight (event P) is .54. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .15.

(a) What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight? (Round your answer to 4 decimal places.)

(b) In this problem, are D and P independent?

28)       If Punxsutawney Phil sees his shadow on February 2, then legend says that winter will last 6 more weeks. In 118 years, Phil has seen his shadow 104 times.

(a) What is the probability that Phil will see his shadow on a randomly chosen Groundhog Day? (Round  your answer to 4 decimal places.)

(b) What kind of probability is this?

29)       Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center.

(a) Calculate the FPCF for this sample. (Round your answer to 4 decimal places.)

(b) Should the population be considered effectively infinite?

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