Binomial and Geometric Distribution

Using Inequality Notation

100

What values of the discrete variable X would be included in x< 4?

0, 1, 2, 3

200

P(x > 3) is equivalent to 1 - P(x <= 3) when x represents a discrete variable. What is P(x >= 7) equivalent to when x represents a discrete variable?

1 - P(x <= 6)

300

Suppose the probability of failing a lie detector test is 30%. In a 12-man jury, what is the probability that more than 3 people will fail the lie detector test?

.507

400

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 greater than 3.

.766

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 within 1 standard deviation of its mean.

.793

Binomial Distribution

100

The probability that a 3 year old battery works is .7 and a graphing calculator requires 4 batteries to work. Ms Y finds 4 batteries that are 3 years old in the back of her closet. What is the probability that she puts them in a calculator and it works?

.2401

200

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?

.061

300

If P(X=x) =(n choose 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?

.3439

500

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 no one uses his or her blinker when changing lanes?

0.6561

Geometric Distribution

100

Cuong takes a guess on a multiple choice test in Vietnamese. Each question has options a, b, c, d, e, and f. What is the average number of questions he has to answer before he gets one correct?

6

200

On Cuong's multiple choice test (with 6 possible choices), what is the probability that the first time he gets one right is on the 4th question?

.096

300

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

.04117

400

A quarterback completes 47% of his passes. Construct a probability distribution table (out of n = 5) for the number of passes attempted before the quarterback has a completion

n =  1      2      3       4     5 

p = .47 .2491 .1320 .07 .037

500

Can the Geometric Distribution have a probability for P(X=0)?

No.  Only 1 or more. 

Normal Approximation

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

200

The probability that a person who is lady who is at least 40 years old colors her hair is .64. Suppose you survey 1000 women. What is the probability that more than 400 DO NOT color their hair.

.0038

300

According to the CDC, 20% of teenagers vape. Suppose that 300 teenagers walked into school on a given day. What is the probability that more than 50 of them vape?

.9265

400

Explain why the normal approximation can not be used when n = 100 p = .95

nq <= 10

500

What is the standard deviation (to the nearest 10th) for a bag of 1000 M&M's with 25% green candies?

13.7

Probability Distribution

100

See the probability table on the number of goals scored in a KHS soccer match.

What is the mean, or expected number of goals?

E(X) =1.45

200

See the probability table on the number of goals scored in a KHS soccer match.

What is the variance of the number of goals?

Var (X) = 0.947

300

See the probability table on the number of goals scored in a KHS soccer match.

What is the standard deviation of the number of goals?

Standard deviation = 0.9734

400

See the probability table on the number of goals scored in a KHS soccer match.

If we play 20 games per season, how many goals should the KHS soccer team make?

number per 20 game season = 29

500

Is the probability distribution given by Ms. Y a valid distribution?

No.  Do not add up to 1.0.