Chapter 4 College Statistics

Vocab

100

What is a finite or countable # of possible outcomes that can be listed?

discrete random variable

200

What is an uncountable # of outcomes represented by an interval on a number line?

continuous

300

What does n, p, q, and x represent?

n= number of trials x= the number of successes in n trials p=probability of success in a single trial q= probability of failure in a single trial

400

What is a numerical value associated with each outcome of a probability experiment?

Random Variable

500

What lists each possible value the random variable can assume together with it's probability?

Discrete Probability Distribution

Discrete + Continuous

100

x represents the distance from the earth to the moon

Continuous

200

x represents the number of rainy days in the month of September in New York

Discrete

300

x represents the amount of money you make each week

discrete

400

x represents the length of time it takes to get home from school

continuous

500

x represents the acceleration of a car as it goes from 0 mph to 60 mph

continuous

Geometric + Poisson

100

The probability of an enemy aircraft penetrating friendly airspace is 0.01. What's the probability that the first penetration of friendly airspace is accomplished by the 80th aircraft to attempt the penetration of friendly aircraft?

P(80,0.01)= 0.01(1-0.01)^80-1 = .00452

200

A complex software system averages 7 errors per 5,000 lines of code. What is the probability of exactly 2 errors in 5,000 lines of randomly selected code?

P(2,7)= (e^-7)(7^2) / 2! = 0.022

300

A cereal maker places a game piece in it's cereal box. The probability of winning a prize is 1 in 4. What is the probability that you win your first prize within your fourth box of cereal?

P(4)= (1/4)(3/4)^3 = .10546875

400

Over a long period of time, it has been noted that on Friday's 25% of customers at the drive in window at the bank make deposits. What's the probability that it takes 4 customers at the drive-in window before the first one makes a deposit.

P(4)= (.75)^4-1 (.25) = .0117

500

The mean number of accidents per month at an intersection is 3. What's the probability that in any given month more than 2 accidents will occur?

poissionpdf(3,2) + poissonpdf(3,1) + poissonpdf(3,0) = .4231900811 1- .4231900811 = .5768099189

Binomial Probability

100

Which fraction represents the probability of obtaining exactly 8 heads in 10 tosses of a fair coin?

45/1024

200

If a fair die is tossed 5 times, what is the probability of getting exactly 3 even numbers?

10/32

300

25% of unicorns like celery. You randomly select 18 unicorns to name their favorite vegetable. Find the probability that 4 unicorns say they like celery.

.2129801598

400

60% of mermaids want to be human. If you interview 7 mermaids, what is the probability that less than 2 want to be human?

.0188416

500

25% of unicorns like celery. You randomly select 18 unicorns to name their favorite vegetable. Find the probability that less than 4 unicorns say they like celery.

.305689170

Expected Value

100

The expected value of a discrete random variable is equal to the ______ of the random variable?

mean

200

In a lottery, 10,000 tickets are sold at $2 with a prize of $5,000 for one winner. What can you expect to gain from buying one ticket?

$-1.50

300

Concessionaires know that attendance at a football stadium will be 10,000 on a clear day, 5,000 if there is light snow, and 3,000 if there is heavy snow. The probability of clear skies, light snow, or heavy snow on any particular day is .7, .25, and .05 respectively. What average attendance should be expected for the season?

8,400 people

400

At a raffle, 1,000 tickets are sold at $1 each for two prizes of $400 and $200. You buy one ticket. What is the expected value of your gain?

$-00.40

500

Your father offers to flip a coin once and if the coin lands on heads he will give you $50, but if it lands on tails you will get nothing. Your mother offers to roll a die one time and give you $5 for each spot that turns up. Which of these is the better offer?

Your father's offer is better. It has an expected value of $25, while your mothers offer only has an expected value of $17.50.