10.2 Review questions

Collaborative statistics homework Page 1 / 1

Copy of Review Questions module m17021 (http://cnx.org/content/ m17021/) from Collaborative Statistics by Dean and Illowsky http://cnx.org/content/col10522/ , 12/18/2008 . The FORMAT only of the question numbering has been changed.

The next three questions refer to the following information:

In a survey at Kirkwood Ski Resort the following information was recorded:

Sport participation by age
	0 – 10	11 - 20	21 - 40	40+
Ski	10	12	30	8
Snowboard	6	17	12	5

Suppose that one person from of the above was randomly selected.

Find the probability that the person was a skier or was age 11 – 20.

REVIEW QUESTION 1 Solution : $\frac{77}{100}$

Find the probability that the person was a snowboarder given he/she was age 21 – 40.

REVIEW QUESTION 2 Solution : $\frac{12}{42}$

Explain which of the following are true and which are false.

A
Sport and Age are independent events.
B
Ski and age 11 – 20 are mutually exclusive events.
C
$P (Ski and age 21 - 40) < P (Ski ∣ age 21 - 40)$
D
$P (Snowboard or age 0 - 10) < P (Snowboard ∣ age 0 - 10)$

Review question 3 solution

A
False
B
False
C
True
D
False

The average length of time a person with a broken leg wears a cast is approximately 6 weeks. The standard deviation is about 3 weeks. Thirty people who had recently healed from broken legs were interviewed. State the distribution that most accurately reflects total time to heal for the thirty people.

REVIEW QUESTION 4 Solution : $N (180, 16.43)$

The distribution for $X$ is Uniform. What can we say for certain about the distribution for $\bar{X}$ when $n = 1$ ?

A
The distribution for $\bar{X}$ is still Uniform with the same mean and standard dev. as the distribution for $X$ .
B
The distribution for $\bar{X}$ is Normal with the different mean and a different standard deviation as the distribution for $X$ .
C
The distribution for $\bar{X}$ is Normal with the same mean but a larger standard deviation than the distribution for $X$ .
D
The distribution for $\bar{X}$ is Normal with the same mean but a smaller standard deviation than the distribution for $X$ .

REVIEW QUESTION 5 Solution : A

The distribution for $X$ is uniform. What can we say for certain about the distribution for $\sum X$ when $n = 50$ ?

A
The distribution for $\sum X$ is still uniform with the same mean and standard deviation as the distribution for $X$ .
B
The distribution for $\sum X$ is Normal with the same mean but a larger standard deviation as the distribution for $X$ .
C
The distribution for $\sum X$ is Normal with a larger mean and a larger standard deviation than the distribution for $X$ .
D
The distribution for $\sum X$ is Normal with the same mean but a smaller standard deviation than the distribution for $X$ .

REVIEW QUESTION 6 Solution : C

The next three questions refer to the following information:

A group of students measured the lengths of all the carrots in a five-pound bag of baby carrots. They calculated the average length of baby carrots to be 2.0 inches with a standard deviation of 0.25 inches. Suppose we randomly survey 16 five-pound bags of baby carrots.

State the approximate distribution for $\bar{X}$ , the distribution for the average lengths of baby carrots in 16 five-pound bags. $\bar{X} ~$

REVIEW QUESTION 7 Solution : $N (2, \frac{.25}{\sqrt{16}})$

Explain why we cannot find the probability that one individual randomly chosen carrot is greater than 2.25 inches.

Review question 8 solution

We do not know the probability distribution for the underlying population of lengths of the individual carrots.

Find the probability that $\bar{X}$ is between 2 and 2.25 inches.

REVIEW QUESTION 9 Solution : 0.5000

The next three questions refer to the following information:

At the beginning of the term, the amount of time a student waits in line at the campus store is normally distributed with a mean of 5 minutes and a standard deviation of 2 minutes.

Find the 90th percentile of waiting time in minutes.

REVIEW QUESTION 10 Solution : 7.6

Find the median waiting time for one student.

REVIEW QUESTION 11 Solution : 5

Find the probability that the average waiting time for 40 students is at least 4.5 minutes.

REVIEW QUESTION 12 Solution : 0.9431

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Source: OpenStax, Collaborative statistics homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2

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10.2 Review questions

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Review question 3 solution

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B

C

D

A

B

C

D

A

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C

D

Review question 8 solution

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