Normal, Binomial, and Geometric Distribution

Geom/Binom Dist.

Binomial Probability

Geometric Distribution

Normal Approximation

Life of Woyna

100

Suppose X has a binomial distribution with n = 500 and p = .3. Find the mean and standard deviation of the distribution.

Mean =150 Standard Deviation = 10.25

100

The probability that a 3 year old battery works is .7 and a graphing calculator requires 4 batteries to work. Mr. Woyna finds 4 batteries that are 3 years old in the math office. What is the probability that he puts them in a calculator and it works?

.7⁴ = binompdf(4, .7, 4) = .2401

100

Tony takes random guesses on a multiple choice test in Chinese. Each question has options a, b, c, and d. What is the average number of questions he has to answer before he gets one correct?

100

Mr. Woyna plans on racing (beating) Dani in the Lisle 5K. If Mr. Woyna averages 23 minutes with a standard deviation of 3 minutes per 5K and Dani averages 29 minutes with a standard deviation of 4 minutes per 5K. How much on average will Mr. Woyna win by?

29 - 23 = 6 minutes...

100

What is Mr. Woyna's favorite class to teach?

AP Stats!!!

200

Give all 4 conditions for binomial random variables.

BINS (Binary, Independent, "n", success rate)

200

The probability that a telemarketing employee reaches a person is .11. Suppose they call 20 people in a night. What is the probability that they reach 3 or less people?

binomcdf(20, .11, 3) = .829

200

On Tony's multiple choice test (4 choices per question), what is the probability that the first time he gets one right is on the 4th question?

geompdf(.25, 4) = .105

200

Over April's career, she hits the ball in a normal distribution with a mean of 200 feet and a standard deviation of 30 feet. Find the probability that a random hit will go more than 250 feet.

normalcdf(250, 10000, 200, 30) = .0478

200

Where did Mr. Woyna attend graduate school?

Northeastern Illinois

300

Give all conditions needed for a geometric distribution.

Binary, Independent, "until", Success Rate

300

The probability that a telemarketing employee reaches a live person is .11. Suppose they call 20 people in a night. What is the probability that they reach at least 5 people?

1 - binomcdf(20, .11, 4) = .061

300

Julio tends to score once out of every 3 shots he takes on goal. What is the probability that he will score within the first 5 shots of the game?

geometcdf(1/3,5) = .8683

300

5 minutes

300

What is the name of Mr. Woyna's childhood dog? (Hint: it is the name of an Ex-Bear QB)

Cutler

400

(n C 5) p⁵ (.71)⁸ What is n? What is P? What is mean of the distribution?

n = 13 p = .29 Mean = 3.77

400

It is estimated that 10% of drivers turn on their blinker before changing lanes. In a random sample of 4 drivers, what is the probability that at least one person uses his or her blinker when changing lanes?

1 - binom(4, .1, 0) = .3439

400

Cal has a history of making his free throws 45% of the time. What is the probability that he will make his first free throw before his 5th try in a game?

geometcdf(.45, 4) = .908

400

normalcdf(60, 1000, 52, 5) = .055

400

In what year did Mr. Woyna begin teaching at Lisle?

Fall of 2012

500

According to government data, 20% of employed women have never been married. 25 employed women are selected at random. Find the probability that the number of employed women who have never been married is between 1 and 6.

binomcdf(25,.2, 6) - binompdf(25, .2, 0) = .776

500

1 - binomcdf(25, .2, 3) = .766

500

Tara has a history of making her free throws 85% of the time. What is the probability that she will miss her first free throw on her 5th try or after in a game?

1 - geometcdf(.15, 4) = .522

500

normalcdf(-10000, 0, -6, 5) = .8849 or

normalcdf(0, 1000, 6, 5)

88.5%....

500

What high school did he attend?

Oak Forest HS (Home of the Bengals!!)