07 Jan There is sufficient

Week 1 discussion

By the due date assigned, submit your answers to the Discussion Area.

For each week’s assignment, find your assigned letter and complete the problems associated with that letter. If your instructor has not assigned you a letter, please use the first letter of your last name. Please post both of the problems assigned to you.

Post responses to at least two other students on two separate days of the week. You can:

Ask a question about your classmate’s solution

Offer help when you see an error

Seek help in completing your own problems

Remember that non-substantive posts such as “Good job!” will not count toward your participation score.

By the end of the week, please review and comment on the answers provided by at least two of your peers.

MAT2058 Discussion Questions

Week 1

Textbook: Triola, M. F. (2014). Elementary statistics technology update (12th ed.). Boston, MA:

Pearson Education.

An electronic version of this book is available in this classroom.

Instructions:

? In the Course Home announcement area there should be a listing with your name and

letter assigned for the discussion questions. If there is not such a list, then find the first

letter of your last name below, and complete the two discussion problems associated

with this letter.

? Please show all of the steps and processes you used to solve each of your problems.

? Remember to do both of the problems assigned and to respond to two of your

classmates’ solutions.

? Please try to respond to two of your classmates who have had very different

problems than yours assigned to them. You should receive more credit for doing

so.

? In responding to the postings of at least two of your classmates, you can

o ask a question about your classmate’s solution(s)

o offer help when you see an error, or

o seek help in completing your own problems.

Remember that non-substantive posts such as “Good job!” will not count toward your

participation score. Again, try to respond to at least two classmates who have problems

assigned that are quite different from yours.

? Please note that the assigned problems vary in difficulty and the list has been randomly

generated for each of the two assigned problems.

Week 1 Discussion Questions

See the first

instruction on the

previous page.

Please submit the two discussion items

* Researchers test two different blood pressure

medicines to determine effectiveness.

Y: total cost of text books and supplies for courses

Z: method of payment used for textbooks and supplies

a. What is the population?

b. What is the sample?

c. Classify the three variables as nominal, ordinal, discrete or

continuous.

G

Describe whether the following study would most

likely be “observational” or “experimental”, and

why it would be so.

* One group is given Stilbesterol, the other

nothing, to see which grows faster.

&

Identify each of the following as examples of

(1) nominal, (2) ordinal, (3) discrete, or (4) continuous variables:

a. A poll of registered voters as to which candidate they support

b. The length of time required for a wound to heal when a new

medicine is being used

c. The number of televisions within a household

d. The distance first-year college women can kick a football

H

USA Today conducted a survey asking readers,

“What is the most hilarious thing that has ever

happened to you en route to or during a

business trip?”

a. What kind of sampling method is this?

b. Are the results likely to be biased? Explain why

or why not.

&

At a recent track event with 22 runners in the U.A.E., Ahmed ran

the mile in 5 minutes, 40 seconds. The average time for this event

in the U.A.E. is about 5:52, where at this event it was 5 minutes, 45

seconds. Based on this, identify:

• the statistic

• the parameter

I

The formula for the variance of a sample is:

If the sample mean equals 15 in a sample of 5 data

values, find 4 other values of x that will make the

variance equal zero.

&

Using the information from the first question what would be the

sum of the deviations from the mean for this sample of 5 values,

and why is this so?

J

Consider the sample 2, 4, 7, 8, 9, 10. Find the

following:

a. mean,

b. median,

c. mode

d. midrange

&

a. What does it mean for a value to be non-negative?

b. Describe the conditions necessary for the variance to have

the value zero

K

Consider the sample 1, 2, 4, 7, 8, 9, 10, 20.

Find the following:

a. mean

&

For the data set in the first problem, 1, 2, 4, 7, 8, 9, 10, 20, find:

a. The 50th percentile

b. The third quartile point

b. median,

c. mode

d. midrange

c. The 33rd percentile

Week 2 discussion

MAT2058 Discussion Questions

Week 2

Text:

Textbook: Triola, M. F. (2014). Elementary statistics technology update (12th ed.). Boston, MA: Pearson Education.

Instructions:

• In the Course Home announcement area there should be a listing with your name and letter assigned for the discussion questions. If there is not such a list, then find the first letter of your last name below, and complete the two discussion problems associated with this letter.

• Please show all of the steps and processes you used to solve each of the problems.

• Remember to do both of the problems assigned and to respond to two of your classmates’ solutions.

• Please try to respond to two of your classmates who have had very different problems than yours assigned to them. You should receive more credit for doing so.

• In responding to the postings of at least two of your classmates, you can

o ask a question about your classmate’s solution(s)

o offer help when you see an error, or

o seek help in completing your own problems.

Remember that non-substantive posts such as “Good job!” will not count toward your participation score. Again, try to respond to at least two classmates who have problems assigned that are quite different from yours.

• Please note that the assigned problems vary in difficulty and the list has been randomly generated for each of the two assigned problems.

Week 2 Discussion Questions

See the first instruction on

the previous page.

Please submit the two discussion items for your assigned letter.

Provide an example of what differentiates Suppose we want to determine the (binomial) probability (p) of

a “Probability” from a “Probability

getting 6 heads in 12 flips of a 2-sided coin. Using the binomial table

Distribution”. In this example identify

A & in the appendix of the text, what values of n, x, and p would we use

both the probability and the probability

to look up this probability, and what would be the probability?

distribution.

Suppose we want to determine the A social worker is involved in a study about family structure. She

(binomial) probability (p) of getting 2 obtains information regarding the number of children per family for

heads in 5 flips of a 2-sided coin. Using a certain community from the census data. Identify the variable of

B the Binomial Table in the appendix of the & interest, determine whether it is discrete or continuous and list

text, what values of n, x, and p would we some possible values.

use to look up this probability, and what

would be the probability?

Above-average warmth extended over the east and southeast on

Explain why this is or is not a probability January 13, 2005. The day’s forecasted high temperatures in four

distribution. cities in the affected area were as follows.

x 1 2 3 4

P(x) 0.2 0.3 0.4 0.1

C &

a. What is the random variable involved in this study?

b. Is the random variable discrete or continuous? Explain.

Identify the properties that make flipping What does it mean for the trials to be independent in a binomial

D a coin 50 times and keeping track of heads &

experiment?

a binomial experiment.

Provide an example of a probability A die is rolled 20 times and the number of “fives” that occur is

E distribution that has four distinct & reported as being the random variable. Is this a binomial random

outcomes. In this example, please identify variable? Why or why not.

the outcome and the probability of that

outcome occurring.

The employees at a General Motors assembly plant are polled as

What is it that differentiates a binomial they leave work. Each is asked, “What brand of automobile are you

F probability distribution from any other & riding home in?” The random variable to be reported is the number

probability distribution? of each brand mentioned. Is x a binomial random variable? Justify

your answer.

A USA Snapshot titled: “Are you getting a summer job?”

Explain why this is or is not a probability Interviews with high school students produced the following.

distribution,

49% Yes

x 1 2 3 4 & 26% Maybe

G P(x) 0.4 0.3 0.3 0.0 25% No

a. What are the variables involved?

b. Why is this variable not a random variable?

Why is the variable “number of saved If the P(x)’s below represent the probabilities of each outcome,

H telephone numbers on a person’s phone” & explain why this is or is not a binomial probability distribution,

classified as a discrete variable?

x 1 2 3 4

P(x) 0.4 0.3 0.3 0.0

Let x be a random variable with the following probability

distribution:

Provide one example of a discrete

I variable (random or not) and one &

example of a continuous variable.

Does x have a binomial distribution? Justify your answer.

USA snapshot presented a bar graph depicting business travelers’

impression of wait times in airport security lines over the past 12

Explain why this is or is not a probability months. Statistics were derived from Travel Industry Association of

American Business Traveler Survey of 2034 respondents. Could this

distribution.

be a probability distribution? Why or why not.

J &

x 1 2 3 4 Worse – 49%

P(x) 0.2 0.1 0.4 0.2

Same 40%

Better – 11%

A box contains 10 items, of which 3 are The random variable has the following probability distribution:

defective and 7 are non-defective. Two

items are randomly selected, one at a

time, with replacement, and x is the

K number of defective items in the sample. &

To look up the probability of a defective a. Find the mean and standard deviation of xbar.

item being drawn from the box, using a

binomial probability table, what would be

the values of n, x and p to look up?

For the sample of 10 values in the Given the sample 7, 6, 10, 7, 5, 9, 3, 7, 5, 13, find the Standard

L second question, what is the value of &

Deviation, s.

?(x – xbar)?

Explain why this is or is not a probability Start with x = 100 and add four x values to make a sample of five

distribution.

M & data such that the standard deviation of these data equals 0.

x 1 2 3 4

P(x) 0.4 0.3 0.4 -0.1

Suppose we want to determine the In testing a new drug, researchers found that 10% of all patients

(binomial) probability (p) of getting 0

using it will have a mild side effect. A random sample of 12 patients

(zero) heads in 5 flips of a 2-sided coin.

using the drug is selected. If you wanted to find the probability that

Using the Binomial Probability table in the

N & exactly three will have this mild side effect, what would be the

appendix of the text, what values of n, x,

values of n, x, and p that you would use to look this probability up in

and p would we use to look up this

the Binomial Probability table (A-1), AND what would be the

probability, and what would be the

probability?

probability?

Suppose we want to determine the

(binomial) probability (p) of getting 8

heads in 10 flips of a 2-sided coin. Using If x is a binomial random variable, use the binomial table to

O the Binomial Probability table in the & determine the probability of x for each of the following:

appendix of the text, what values of n, x a. n = 10, x = 8, p = 0.3

and p would we use to look up this b. n = 8, x = 7, p = 0.95

probability, and what would be the

probability?

Suppose we want to determine the

(binomial) probability (p) of getting 3 Four cards are selected, one at a time from a standard deck of 52

heads in 15 flips of a 2-sided coin. Using

cards. Let x represent the number of Jacks drawn in a set of 4

the Binomial Probability table in the

P & cards. If the cards are not replaced after each draw, explain why x

appendix of the text, what values of n, x,

is NOT a binomial random variable.

and p would we use to look up this

probability, and what would be the

probability?

“How many TV’s are there in your household?” was one of the

questions on a questionnaire sent to 5000 people in Japan. The

Suppose we want to determine the collected data resulted in the following distribution:

(binomial) probability (p) of getting 4

heads in 10 flips of a 2-sided coin. Using

Q the Binomial Table in the appendix of the &

text, what values of n, x, and p would we

use to look up this probability, and what

would be the probability? One of these households is selected at random.

Week 3 discussion

MAT2058 Discussion Questions

Week 3

Text:

Textbook: Triola, M. F. (2014). Elementary statistics technology update (12th ed.). Boston, MA:

Pearson Education.

Instructions:

• In the Course Home announcement area there should be a listing with your name and letter assigned for the discussion questions. If there is not such a list, then find the first letter of your last name below, and complete the two discussion associated with this letter.

• Please show all of the steps and processes you used to solve each of the problems.

• Remember to do both of the problems assigned and to respond to two of your classmates’ solutions.

• Please try to respond to two of your classmates who have had very different problems than yours assigned to them. You should receive more credit for doing so.

• In responding to the postings of at least two of your classmates, you can

o ask a question about your classmate’s solution(s)

o offer help when you see an error, or

o seek help in completing your own problems.

Remember that non-substantive posts such as “Good job!” will not count toward your participation score. Again, try to respond to at least two classmates who have problems assigned that are quite different from yours.

Please note that the assigned problems vary in difficulty and the list has been randomly generated for each of the two assigned problems.

Revised Week 3 Discussion Questions

See the first instruction

on the previous page.

Please submit the two discussion items for your assigned letter.

Examine the intelligence quotient, or IQ, as it

is defined by the formula:

Assuming a normal distribution, what is the z-score “intelligence quotient = 100 * (mental

A associated with the 90th percentile? &

age/chronological age)”

What would be the IQ if a person’s

chronological age equals their mental age?

&

What percentage of the area would the Empirical

B Rule say is between z = -3.00 and z = +3.00? Given x = 237, ? = 220, and ? = 12.3, find z.

In looking at the properties of the Standard &

Normal Distribution below:

Properties of the Standard Normal Distribution:

1. The total area under the normal curve is

equal to 1.

2. The distribution is mounded and Given that x is a normally distributed random

symmetrical; it extends indefinitely in both

variable with a mean of 28 and a standard

directions, approaching but never touching the

deviation of 7, find the following probability:

horizontal axis.

C

P(x < 28) = P(z< ?) = ? 3. The distribution has a mean of 0 and a standard deviation of 1. 4. The mean divides the area in half—0.50 on each side. 5. Nearly all the area is between z = ?3.00 and z = 3.00. Which of these properties does not necessarily apply to any normal distribution? & How would standard (z) scores of -2.00 and +2.00 be Find the z-score for the standard normal D interpreted using the Standard Normal Distribution distribution where: Table (A-2) in the text? P(z < +a) = 0.8980 E What one characteristic about the Standard Normal & Distribution make it different from any normal Find the z-score for the standard normal distribution? distribution where: P(z < -a) = 0.0721 Find the standard z-score that corresponds to What are the primary advantages of the Standard the following: F Normal Distribution that other normal distributions & Eighty percent of the distribution is below (to do not have? the left of) this value. If the random variable z is the standard normal score Find the (two) z-scores that bound the middle G and a > 0, is it true that P(z > -a) = P(z < a)? Why or & 40% of the standard normal distribution. why not? If n = 100 and p = 0.02 in a binomial experiment, Find the z-score for the standard normal H does this satisfy the rule for a normal approximation? & distribution where: Why or why not? P(z< -a) = 0.2451 If n = 100 and p = 0.05 in a binomial experiment, Find the z-score for the standard normal does this satisfy the rule for a normal approximation? distribution where: I Why or why not? & P(z