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Chapter 5: Q. T5.8 (page 357)
In a class, there are 18 girls and 14 boys. If the teacher selects two students at random to attend a party with the principal, what is the probability that the two students are the same sex?
a.
b.
c.
d.
e.
The probability is
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Preparing for the GMAT A company that offers courses to prepare students for the Graduate Management Admission Test (GMAT) has collected the following information about its customers: are undergraduate students in business, are undergraduate students in other fields of study, and are college graduates who are currently employed. Choose a customer at random.
a. What must be the probability that the customer is a college graduate who is not currently employed? Why?
b. Find the probability that the customer is currently an undergraduate. Which probability rule did you use to find the answer?
c. Find the probability that the customer is not an undergraduate business student. Which probability rule did you use to find the answer?
The partially completed table that follows shows the distribution of scores on the
AP庐 Statistics exam.
Suppose we randomly select a student who took this exam. What鈥檚 the probability that he
or she earned a score of at least?
a.
b.
c.
d.
e.
Treating low bone density Fractures of the spine are common and serious
among women with advanced osteoporosis (low mineral density in the bones). Can taking
strontium ranelate help? A large medical trial was conducted to investigate this question.
Researchers recruited women with osteoporosis who had previously had at least one
fracture for an experiment. The women were assigned to take either strontium ranelate or a
placebo each day. All the women were taking calcium supplements and receiving standard
medical care. One response variable was the number of new fractures over years.
a. Describe a completely randomized design for this experiment.
b. Explain why it is important to keep the calcium supplements and medical care the same
for all the women in the experiment.
c. The women who took strontium ranelate had statistically significantly fewer new
fractures, on average, than the women who took a placebo over a year period. Explain
what this means to someone who knows little statistics.
Taking the train According to New Jersey Transit, the weekday train from Princeton to New York City has a chance of arriving on time. To test this claim, an auditor chooses weekdays at random during a month to ride this train. The train arrives late on of those days. Does the auditor have convincing evidence that the company's claim is false? Describe how you would carry out a simulation to estimate the probability that a train with a chance of arriving on time each day would be late on or more of days. Do not perform the simulation.
Roulette An American roulette wheel has 38 slots with numbers throughand , as shown in the figure. Of the numbered slots, are red, are black, and 鈥攖丑别 and 鈥攁re green. When the wheel is spun, a metal ball is dropped onto the middle of the wheel. If the wheel is balanced, the ball is equally likely to settle in any of the numbered slots. Imagine spinning a fair wheel once. Define events : ball lands in a black slot, and : ball lands in an even-numbered slot. (Treatand as even numbers.)
a. Make a two-way table that displays the sample space in terms of events and .
b. Find and.
c. Describe the event 鈥�and 鈥� in words. Then find the probability of this event.
d. Explain why . Then use the general addition rule to compute .
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