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Chapter 4: Q5 (page 143)
Identifying Probability Values Which of the following are probabilities?
0 3/5 5/3 -0.25 250% 7:3 1 50-50 5:1 0.135 2.017
The probability values are 0, , 1, and 0.135.
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Composite Drug Test Based on the data in Table 4-1 on page 162, assume that the probability of a randomly selected person testing positive for drug use is 0.126. If drug screening samples are collected from 5 random subjects and combined, find the probability that the combined sample will reveal a positive result. Is that probability low enough so that further testing of the individual samples is rarely necessary?
Interpreting Weather While this exercise was being created, Weather.com indicated that there was a 60% chance of rain for the author’s home region. Based on that report, which of the following is the most reasonable interpretation?
a. 60% of the author’s region will get rain today.
b. In the author’s region, it will rain for 60% of the day.
c. There is a 0.60 probability that it will rain somewhere in the author’s region at some point during the day.
In Exercises 25–32, find the probability and answer the questions.. Car Rollovers In a recent year in the United States, 83,600 passenger cars rolled over when they crashed, and 5,127,400 passenger cars did not roll over when they crashed. Find the probability that a randomly selected passenger car crash results in a rollover. Is it unlikely for a car to roll over in a crash?
Acceptance Sampling. With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is found to be okay. Exercises 27 and 28 involve acceptance sampling.
Something Fishy: The National Oceanic and Atmospheric Administration (NOAA) inspects seafood that is to be consumed. The inspection process involves selecting seafood samples from a larger “lot.” Assume a lot contains 2875 seafood containers and 288 of these containers include seafood that does not meet inspection requirements. What is the probability that 3 selected container samples all meet requirements and the entire lot is accepted based on this sample? Does this probability seem adequate?
Using Probability to Form Conclusions. In Exercises 37–40, use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion.
Buckle Up A study of the effect of seatbelt use in head-on passenger car collisions found that drivers using a seatbelt had a 64.1% survival rate, while drivers not using a seatbelt had a 41.5% survival rate. If seatbelts have no effect on survival rate, there is less than a 0.0001 chance of getting these results (based on data from “Mortality Reduction with Air Bag and Seat Belt Use in Head-on Passenger Car Collisions,” by Crandall, Olson, Sklar, American Journal of Epidemiology, Vol. 153, No. 3). What do you conclude?
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