stat exam 2

what is the range of Pearsons coefficient skewness

-3 to 3

The events XX and YY are mutually exclusive. Suppose P(X) = 0.07 and P(Y) = 0.05. What is the probability of either XX or YY occurring?

.07 + .05 = .12

A National Park Service survey of visitors to the Rocky Mountain region revealed that 50% visit Yellowstone, 40% visit the Tetons, and 35% visit both. What is the probability a vacationer will visit at least one of these attractions?

.50 + .40 = .90 .35 - .90 = .55

A student is taking two courses, history and math. The probability the student will pass the history course is 0.55, and the probability of passing the math course is 0.64. The probability of passing both is 0.43. What is the probability of passing at least one

.55+.64= 1.19 1.19-.43= .76

Recent surveys indicate 60% of tourists to China visited the Forbidden City, the Temple of Heaven, the Great Wall, and other historical sites in or near Beijing. Forty percent visited Xi'an with its magnificent terra-cotta soldiers, horses, and chariots, which lay buried for over 2,000 years. Thirty percent of the tourists went to both Beijing and Xi'an. What is the probability that a tourist visited at least one of these places?

.60 + .40 - .30 = .70

Suppose P(X1) = 0.75 and P(Y2 | X1) = 0.40.What is the joint probability of X1 and Y2?

.75 x .40 = .30

All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is 0.80, the probability the second truck is available is 0.55, and the probability that both trucks are available is 0.44. What is the probability neither truck is available?

.80 + .55 = 1.35 1.35 - .44 = .91 1 - .91 = .09

You take a trip by air that involves three independent flights. If there is an 80% chance each specific leg of the trip is on time, what is the probability all three flights arrive on time?

.80 x .80 x .80= .512

Assume the likelihood that any flight on Delta Airlines arrives within 15 minutes of the scheduled time is 0.90. We randomly selected a Delta flight on four different days. What is the likelihood all four of the selected flights arrived within 15 minutes of the scheduled time?

.90 ^4= .6561

multiplication formula

m x n , there are M ways of doing one thing and N ways of doing another

law of large numbers

more times something happens the closer to its true probability it will be

and means...

multiply

conditional probability

the probability that one event happens given that another event is already known to have happened

box trifecta

top 3 horses in any order, combination

straight trifecta

top 3 horses in correct order, permutation

box superfecta

top 4 horses in any order, combination

straight superfecta

top 4 horses in correct order, permutation

negative skew

trails to the left, mean over medium

positively skewed

trails to the right, median over mean

maximin

worst case scenario, hate risk

choices

you have control

complement rule of addition

must be mutually exclusive and collectively exhaustive, determine the probability of an event happening by what didn't happen, ~A = everything but A, P(A)=1-P(~A)

special rule of addition

must be mutually exclusive, P(A or B)= P(A) + P(B)

classical probability must be

mutually exclusive and collectively exhaustive

Pearsons value closer to -3

negative skew

There are 100 employees at Kiddie Carts International. Fifty-seven of the employees are hourly workers, 40 are supervisors, two are secretaries, and the remaining employee is the president. Suppose an employee is selected: What is the probability the selected employee is an hourly worker?

57/100 = .57

Armco, a manufacturer of traffic light systems, found that under accelerated-life tests, 95% of the newly developed systems lasted three years before failing to change signals properly. If a city purchased four of these systems, what is the probability all four systems would operate properly for at least three years? What rule is this?

.95 ^4 = .8145 special rule of multiplication

Assume the likelihood that any flight on Delta Airlines arrives within 15 minutes of the scheduled time is 0.90. We randomly selected a Delta flight on four different days. What is the likelihood at least one of the selected flights did not arrive within 15 minutes of the scheduled time?

1 - .6561 = .3439

Assume the likelihood that any flight on Delta Airlines arrives within 15 minutes of the scheduled time is 0.90. We randomly selected a Delta flight on four different days. What is the likelihood that none of the selected flights arrived within 15 minutes of the scheduled time?

1 - .90 = .01 .01 ^4 = .0001

There are 100 employees at Kiddie Carts International. Fifty-seven of the employees are hourly workers, 40 are supervisors, two are secretaries, and the remaining employee is the president. Suppose an employee is selected: What is the probability the selected employee is neither an hourly worker nor a supervisor?

1 - .97 = .03

The events XX and YY are mutually exclusive. Suppose P(X) = 0.07 and P(Y) = 0.05. What is the probability that neither XX nor YY will happen?

1-.12= .88

moderate skewness

1.63

percentile

100 equal size pieces

A pollster randomly selected four of 10 available people.How many different groups of four are possible?

10c4= 210

There are 20 families living in the Willbrook Farms Development. Of these families, 12 prepared their own federal income taxes for last year, five had their taxes prepared by a local professional, and the remaining three by H&R Block. What is the probability of selecting a family that prepared their own taxes?

12/20 = .6

There are 20 families living in the Willbrook Farms Development. Of these families, 12 prepared their own federal income taxes for last year, five had their taxes prepared by a local professional, and the remaining three by H&R Block. What is the probability of selecting two families, both of which prepared their own taxes?

12/20 x 11/19 = .3473

There are 20 families living in the Willbrook Farms Development. Of these families, 12 prepared their own federal income taxes for last year, five had their taxes prepared by a local professional, and the remaining three by H&R Block. What is the probability of selecting three families, all of which prepared their own taxes?

12/20 x 11/19x 10/18 = .1929

A representative of the Environmental Protection Agency (EPA) wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples.How many different samples are possible?

15c10= 3003

Three defective electric toothbrushes were accidentally shipped to a drugstore by Cleanbrush Products along with 17 nondefective ones. What is the probability the first two electric toothbrushes sold will not be defective?

17/20 x 16/19 = .7158

A large company must hire a new president. The Board of Directors prepares a list of five candidates, all of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to select the president by lottery.

2/5 = .40

There are 20 families living in the Willbrook Farms Development. Of these families, 12 prepared their own federal income taxes for last year, five had their taxes prepared by a local professional, and the remaining three by H&R Block. What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block?

20 - 3 = 17 17/20 x 16/19 = .7157

skewness formula

3(x-median)/standard dev

Three defective electric toothbrushes were accidentally shipped to a drugstore by Cleanbrush Products along with 17 nondefective ones.a. What is the probability the first two electric toothbrushes sold will be returned to the drugstore because they are defective?

3/20 x 2/19 = .0158

b. 10P9

3628800

24!/22!

552

c. 8C5

56

There are 100 employees at Kiddie Carts International. Fifty-seven of the employees are hourly workers, 40 are supervisors, two are secretaries, and the remaining employee is the president. Suppose an employee is selected: What is the probability the selected employee is either an hourly worker or a supervisor?

57/100 + 40/100 = .97

general rule of multiplication

P(A and B) = P(A) x P(B I A), probability of event B is affected by event A

special rule of multiplication

P(A and B) = P(A) x P(B), events A and B must be independent

general rule of addition

P(A or B) = P(A) + P(B) - P(A and B), used when there is going probability, must be collectively exhaustive

2 categories of probability

objective and subjective

states of nature

out of your control

formula for low outlier

Q1 - (1.5 x interquartile range)

how to find interquartile range

Q1-Q3

formula for high outlier

Q3 + (1.5 x interquartile range)

pearsons value closer to 3

positive skew

objective

real numbers, facts

empirical

relative frequency being used as probability, law of large numbers

payoffs

result of choices

Pearsons value that is close to 0

symmetrical

how is the outlier found

the difference between quartile 3 and quartile 1

what is skewness

the lack of symmetry of a distribution

joint probability

the probability of two events occurring together

A baseball player gets a hit in 34 out of 110 times at bat. The probability is 0.31 that he gets a hit in his next at bat.

empirical

d. The probability of an earthquake in northern California in the next 10 years above 11.0 on the Richter Scale is 0.63.

empirical

decisions making strategies

emv, maximin, maximax

mutually exclusive

events that cannot occur at the same time. is it impossible for both to happen??

classical

everyone has the same chance, # of favorable outcomes/# of possible outcomes

subjective

feelings, not math, opinions

outlier

inconsistent with the rest of data, extreme

if something gets replaced its....

independent

or means...

add

combination

arrangement of data does not matter, nCr

Permutation

arrangement of data matters, nPr

collectively exhaustive

at least one of the events must occur when an experiment is conducted

emv

balanced value table

maximax

best case scenario, love risk

elements of a decision

choices, states of nature, payoffs

b. A eight-member committee of students is formed to study environmental issues. What is the likelihood that any one of eight are randomly chosen as the spokesperson.

classical

c. You purchase a ticket for the Lotto Canada lottery. Over eleven million tickets were sold. What is the likelihood you will win the $4 million jackpot?

classical

two subcategories of objective

classical and empirical

event

collection of one or more outcomes

decile

divides into 10

quartile

divides into 4