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An Olympic archer is able to hit the bull's-eye \(80 \%\) of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what's the probability of each of the following results? a. Her first bull's-eye comes on the third arrow. b. She misses the bull's-eye at least once. c. Her first bull's-eye comes on the fourth or fifth arrow. d. She gets exactly 4 bull's-eyes. e. She gets at least 4 bull's-eyes. f. She gets at most 4 bull's-eyes.

It is generally believed that nearsightedness affects about \(12 \%\) of all children. A school district tests the vision of 169 incoming kindergarten children. How many would you expect to be nearsighted? With what standard deviation?

A certain tennis player makes a successful first serve \(70 \%\) of the time. Assume that each serve is independent of the others. If she serves 6 times, what's the probability she gets a. all 6 serves in? b. exactly 4 serves in? c. at least 4 serves in? d. no more than 4 serves in?

A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in 1 of every 8 frogs. He collects and examines a dozen frogs. If the frequency of the trait has not changed, what's the probability he finds the trait in a. none of the 12 frogs? b. at least 2 frogs? c. 3 or 4 frogs? d. no more than 4 frogs?

Based on concerns raised by his preliminary research, the biologist in Exercise 38 ?decides to collect and examine 150 frogs. a. Assuming the frequency of the trait is still 1 in 8 , determine the mean and standard deviation of the number of frogs with the trait he should expect to find in his sample. b. Verify that he can use a Normal model to approximate the distribution of the number of frogs with the trait. c. He found the trait in 22 of his frogs. Do you think this proves that the trait has become more common? Explain.

A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The average size of classes that meet there is \(188,\) and we can assume that about \(13 \%\) of students are left-handed. What's the probability that a right-handed student in one of these classes is forced to use a lefty arm tablet?

A newly hired telemarketer is told he will probably make a sale on about \(12 \%\) of his phone calls. The first week he called 200 people, but only made 10 sales. Should he suspect he was misled about the true success rate? Explain.

The euro Shortly after the introduction of the euro coin in Belgium, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 140 = heads-that's \(56 \%\) heads. Do you think this is evidence that spinning a euro is unfair? Explain.

A basketball player who ordinarily makes about \(55 \%\) of his free throw shots has made 4 in a row. Is this evidence that he has a "hot hand" tonight? That is, is this streak so unusual that it means the probability he makes a shot must have changed? Explain.

The basketball player in Exercise 55 has new sneakers, which he thinks improve his game. Over his past 40 shots, he's made 32 -much better than the \(55 \%\) he usually shoots. Do you think his chances of making a shot really increased? In other words, is making at least 32 of 40 shots really unusual for him? (Do you think it's his sneakers?)