Assume that 21% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:

a. There are some lefties (\( \geq \)1 ) among the 5 people.

b. There are exactly 3 lefties in the group.

c. There are at least 4 lefties in the group.

d. There are no more than 2 lefties in the group.

e. How many lefties do you expect?

f. With what standard deviation?

A point on a meter stick is choosen at random. What is the probability that the choosen point is between\( 15 cm \)and\( 32 cm \)on the meter stick? (A meter stick is\( 100 \)cm long.)

An Olympic archer is able to hit the bull's-eye 82% of the time. Assume each shot is independent of the others. She shoots 5 arrows.

a) How many bull's-eyes do you expect her to get?

b) What is the standard deviation?

c) If she keeps shooting arrows until she hits the bull's-eye, how long do you expect it will take?

An Olympic archer is able to hit the bull's-eye 86% of the time. Assume each shot is independent of the others. She shoots 5 arrows.

a) How many bull's-eyes do you expect her to get?

b) What is the standard deviation?

c) If she keeps shooting arrows until she hits the bull's-eye, how long do you expect it will take?

A fair die is rolled three times. A 5 is considered "success," while all other outcomes are "failures." Find the probability of 3 successes.

The probability of 3 successes is

(Type an integer or a simplified fraction.)