binomial distribution and normal distribution*Section 6.1 numbers 8, 12, 16, 20a, c-e,

In Problems 8, determine whether the random variable is discrete or continuous. In each case, state the possible values of

the random variable.

8.

• (a)The number of defects in a roll of carpet.

• (b)The distance a baseball travels in the air after being hit.

• (c)The number of points scored during a basketball game.

• (d)The square footage of a house.

In Problems 12, determine whether the distribution is a discrete probability distribution. If not, state why

12.

x P(x)

1 0

2 0

3 0

4 0

5 1

In Problems 16, determine the required value of the missing probability to make the distribution a discrete probability

distribution.

16.

x P(x)

0 0.30

1 0.15

2 ?

3 0.20

4 0.15

5 0.05

20.a, c-e,

Waiting in Line A Wendy’s manager performed a study to determine a probability distribution for the number of people, X,

waiting in line during lunch. The results were as follows:

x P(x)

0 0.011

1 0.035

2 0.089

3 0.150

4 0.186

5 0.172

6 0.132

7 0.098

8 0.063

9 0.035

10 0.019

11 0.004

12 0.006

• (a)Verify that this is a discrete probability distribution.

• (c)Compute and interpret the mean of the random variable X.

• (d)Compute the standard deviation of the random variable X.

• (e)What is the probability that eight people are waiting in line for lunch?

*Section 6.2 – numbers 10, 36

In Problems 10, determine which of the following probability experiments represents a binomial experiment. If the probability

experiment is not a binomial experiment, state why.

10.A poll of 1200 registered voters is conducted in which the respondents are asked whether they believe Congress should

reform Social Security.

36.Smokers According to the American Lung Association, 90% of adult smokers started smoking before turning 21 years old. Ten

smokers 21 years old or older are randomly selected, and the number of smokers who started smoking before 21 is recorded.

• (a)Explain why this is a binomial experiment.

• (b)Find and interpret the probability that exactly 8 of them started smoking before 21 years of age.

• (c)Find and interpret the probability that fewer than 8 of them started smoking before 21 years of age.

• (d)Find and interpret the probability that at least 8 of them started smoking before 21 years of age.

• (e)Find and interpret the probability that between 7 and 9 of them, inclusive, started smoking before 21 years of

age.

*Section 7.1 – numbers 26, 36

In Problems 26, the graph of a normal curve is given. Use the graph to identify the values of µand s.

36.

You Explain It! Miles per Gallon Elena conducts an experiment in which she fills up the gas tank on her Toyota Camry 40 times

and records the miles per gallon for each fillup. A histogram of the miles per gallon indicates that a normal distribution

with a mean of 24.6 miles per gallon and a standard deviation of 3.2 miles per gallon could be used to model the gas mileage

for her car.

• (a)The figure represents the normal curve with µ = 24.6 miles per gallon and s = 3.2 miles per gallon. The area under

the curve to the right of x = 26 is 0.3309. Provide two interpretations of this area.

•

• (b)The figure at the top of the next column represents the normal curve with µ = 24.6 miles per gallon and s = 3.2

miles per gallon. The area under the curve between x = 18 and x = 21 is 0.1107. Provide two interpretations of this area.

*Section 7.2 – numbers 20, 24, 28, 34

In Problems 20-28, find the value of za.

20.z 0.02

In Problems 24, assume that the random variable X is normally distributed, with mean µ = 50and standard deviation s = 7.

Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded.

24.P(X > 65)

28.P(56 < X < 68)

In Problems 34, assume that the random variable X is normally distributed, with mean µ = 50and standard deviation s = 7. Find

each indicated percentile for X.

34.The 90th percentile

*Section 7.4 – numbers 22, 28

In Problems 22, find the value of za.

22.z 0.15

In Problems 28, assume that the random variable X is normally distributed, with mean µ = 50and standard deviation s = 7.

Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded.

28.P(56 < X < 68)