07 Jan What percentage of the

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.

A) What percentage of the households have at least one TV?

B) What percentage of the households have at most 3 TV’s?

In the formula for the variance ? (x – In testing a new drug, researchers found that 20% of all patients

R µ)^2/n, what is the sum if we don’t square using it will have a mild side effect. A random sample of 25

the (x – µ) values? [Hint: There is a special patients using the drug is selected. Find the mean and standard

name for this sum.] deviation of patients having a mild side effect.

Suppose we want to determine the Learning is a lifetime activity. For some, it means learning from

(binomial) probability (p) of getting 5 everyday experiences; for others, it means taking classes in a more

heads in 15 flips of a 2-sided coin. Using traditional atmosphere. The percentage of people participating in

the Binomial table in the appendix of the organized learning situations during 2002 for each age group is

text, what values of n, x, and p would we reported here by NIACE.

S use to look up this probability, and what

would be the probability?

Is this a probability distribution? Explain why or why not.

Consider the binomial distribution where The customers at a local appliance store are polled as they leave the

T n = 11 and p = 0.05. store. Each is asked, “What brand of appliance do you prefer?” The

Find the mean and standard deviation of random variable x to be reported is whether the appliance brand is

this binomial distribution. Frigidaire. Is x a binomial variable? Justify your answer.

What differentiates the two formulas The Empirical Rule indicates that we can expect to find what

U ? (x – xbar)^2/n-1 from ? (x – µ)^2/n, &

proportion of the sample included between ± 1 standard deviation?

and why the difference?

In the formula for the variance of values The Empirical Rule indicates that we can expect to find what

proportion of the sample included within + or – 2 sd?

V in a sample, ? (x – xbar)^2/n-1, what is &

required for the variance to equal zero?

A box contains 10 items, of which 3 are

defective and 7 are non-defective. Two

items are randomly selected, one at a

W time, with replacement, and x is the & For the first question about the box containing 10 items of which 3

number of defectives in the sample of are defective, what is the probability of any one selected item being

two. Explain why x is a binomial random non-defective?

variable.

Bill has completed a 10-question multiple-

choice test on which he answered 7

questions correctly. Each question had

one correct answer to be chosen from five

alternatives. Bill says that he answered the

test by randomly guessing the answers

without reading the questions or answers. The mean lifetime of a certain tire is 30,000 miles and the standard

Define the random variable x to be the deviation is 2500 miles.

X number of correct answers on this test, &

and construct the probability distribution If we assume nothing about the shape of the distribution,

if the answers were obtained by random approximately what percentage of all such tires will last between

guessing. 25,000 and 37,500 miles?

• What is the probability that Bill

guessed 7 of the 10 answers

correctly?

Y In the formula ? (x – µ)^2/n for the &

variance, in what cases would we divide According to Chebyshev’s theorem, what proportion of a distribution

by n-1 instead of n? will be within k = 4 standard deviations of the mean? Show all work

as to how to find this.

What percentage of the distribution will According to Chebyshev’s theorem for any distribution (normal or

be within 3 standard deviations of the

Z & not), what percentage of a distribution will be more than 3 standard

mean according to the Empirical Rule?

deviations from the mean?

(for normally distributed data)