Binomial Distribution

Consider two exams and which one has higher. 1. 10 questions true/false; P(correct=0.5) 2. 10 questions multiple choice; P(correct=0.25) Which of the following statements are true regarding the number of correct responses? a. The T/F test has a higher mean and more variability in the responses than the multiple choice test b. The T/F test has a higher mean and less variability in responses than the multiple choice test c. The T/F test has a lower mean and more variability in responses than the multiple choice test d. The T/F test has a low mean and less variability in responses than the multiple choice test.

a mean 1 = (n)(p) = (10)*(0.5)=5 mean 2 = (n)(p) = (10)*(0.25)=2.5 SD1 = sqrt(n*p*(1-p)) SD2 = sqrt(n*p*(1-p))

The binomial distribution is a. probability distribution for a continuous random variable b. probability distribution for a discrete random variable c. probability distribution for a normal random variable d. not probability distribution

b

Discrete random variables: --> how many games do I score in a 9 game season? ____ distribution --> how many are until my first goal? ____ distribution --> how many goals do I score in a game? ___ distribution

binomial, geometric, poisson

In gardening, the probability that a randomly selected seed germinates is 0.5. Consider a small sample of 8 seeds, and assume that whether or not one seed germinates is independent of another seed germinating. What is the distribution of the random variable X= the number of seeds that germinate out of 8? a. X ~ Bin (4, 1.41) b. X ~ N (4, 1.41) c. X ~ Bin (8, 0.5) d. X ~ Bin (8, 0.5)

c

Assume the probability that I get stopped at a traffic light is constant (p=0.3) and that whether or not I get stopped at one stop light is independent of whether or not I get stopped at another. Which of the following scenarios meet the criteria for the binomial distribution? A. x=number of times I am stopped by a traffic light in one day B. x= whether or not I am stopped by a traffic light C. x= number of times I am stopped by a traffic light during my daily commute in which I drive through three lights D. X= number lights I drive through until I get stopped for the first time by a traffic light

c - number of trails is FIXED

We use binomial distribution for ____ categorical variables (it has one of __ possible outcomes).

dichotomous, 2

Conditions for binomial distribution: 1) Trials are ____: the result of 1 trial does not depend on the results of the other trial 2) The number of ___ is FIXED. 3) Each trial has __ possible outcomes: "___" or "___" 4) Each trial has the same ___ of success.

independent, trials, two, success, failure, probability

The binomial random variable is characterized by TWO parameters

n, p

Continuous random variables --> __ --> __ (t-distribution) --> __ (chi-squared distribution) --> __ (F-distribution)

normal, t, x^2, F

The binomial random variable X is the number of ___ in the n trials.

successes

Consider a binomial distribution in order to model the distribution of the number of games in which a player of interest scores (out of a 9 game season) 1. Each game is a trial, and the number of ___ is FIXED at __ games. 2. Each game (trial) has ___ possible outcomes: score ("___") and don't score ("__") 3. For this to be an accurate model: --> the 9 games in the season must be ____ (the result of one game does not depend on the results of other games). --> the player should have the same ____ of scoring in each game.

trials, 9, 2, success, failure, independent, probability