ch 6 practice problems

The area that lies to the right of -1.82

.9656

In one city, 21% of the population is under 25 years of age. Three people are selected at random from the city. Find the probability distribution of X, the number among the three that are under 25 years of age.

0- 0.4930 1-0.3932 2- 0.1045 3- 0.0093

When a coin is tossed four times, sixteen equally likely outcomes are possible as shown be. Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.

0- 1/16 1- 1/4 2- 3/8 3- 1/4 4- 1/16

Police estimate that 25% of drivers drive without their seat belts. If they stop 6 drivers at random, find the probability that all of them are wearing their seat belts.

0.178

In one region, the September energy consumption levels for single-family homes are normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.

0.1971

The weekly salaries of elementary school teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected elementary school teacher earns more than $525 a week?

0.2177

An archer is able to hit the bull's-eye 55% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

0.2627

A basketball player has made 70% of his foul shots during the season. If he shoots 3 foul shots in tonight's game, what is the probability that he makes all of the shots?

0.343

For a normal distribution, find the probability that an observation falls within 0.92 standard deviations of the mean. Sketch a graph and shade the appropriate region.

0.6424 u-0.92SD u+0.92SD

The percent of the voting-age population that is registered to vote for the 50 states and the District of Columbia has a mean of 65% with a standard deviation of 7.1. Assuming that the distribution is normal, what percentage of states had between 50 and 70 percent of it's voting-age population who are registered to vote?

0.74

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

2.28%

A speed-dating agency claims that 80% of the participants in its speed-dating evenings leave with at least one second date arranged. Suppose that 170 people participate in a speed-dating evening. Let X be the number who leave with at least one second date arranged. Assume that this scenario satisfies the conditions for the binomial distribution and use the normal distribution approximation to give an interval in which you would expect X almost certainly to fall, if it is true that Q

(120,152)

Find the z-score having area 0.09 to its left under the standard normal curve.

-1.34

According to a college survey, 22% of all students work full time. Find the standard deviation for the random variable X, the number of students who work full time in samples of size 16.

1.66

A die is rolled 10 times and the number of times that two shows on the up face is counted. If this experiment is repeated many times, find the mean for the random variable X, the number of twos thrown out of ten tosses.

1.67

On a multiple choice test with 16 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the random variable X, the number of correct answers.

1.732

When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. Let X denote the absolute value of the difference of the two numbers. Find the probability distribution of X. Give the probabilities as decimals rounded to three decimal places.

1/16-1/4

According to a college survey, 22% of all students work full time. Find the mean for the random variable X, the number of students who work full time in samples of size 16.

3.52

X = number of rainy days during the first 10 days of January in one city, given that it rains on 20% of days in January in that city.

Conditions for binomial distribution are not satisfied. Trials are not independent. The chance of rain on any given day depends on whether it rained the previous day.

A polling agency in one city randomly selects 1000 registered voters from a pool of 385,600 registered voters of whom 17% are African American. X = number of African Americans in the sample.

Conditions for binomial distribution are satisfied.

Which of the following is not true about the binomial distribution?

The random variable is continuous