Binomial and Geometric Review

Binomial, Geometric or Neither

100

Flipping a coin until you get a head.

Geometric

200

Dealing cards to a person until they get an Ace

Neither

300

Asking 300 people if they like sledding. 

Binomial

400

Taking a sample of 150 people to see how many people celebrate Christmas.

Neither

500

Asking 200 siblings if they have Type 0 blood

Neither (not independent)

Binomial Distribution

100

There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will snow exactly 2 days.

binompdf (n=25, p=.1, x=2)

200

There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will snow less than 4 days.

binomcdf (n=25, p=.1, x = 3)

300

There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will snow more than 4 days.

1 - binomcdf(n=25, p=.1, x=4)

400

There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will snow a minimum of 5 days

1 - binomcdf(n=25, p=.1, x = 4)

500

There is a 10% chance of snow on a given day in December. Find the probability that in a random sample of 25 days in December, it will not snow more than 15 days.

1-binomcdf(n=25, p=.9, z =15)

OR

binomcdf (n=25, p=.1, x= 10)

Geometric Distribution

100

There is a 10% chance of snow on a given day in December. Find the probability that the first day of snow is the 8th day you sample.

geompdf(p=.1, r=8)

200

There is a 10% chance of snow on a given day in December. Find the probability that the first day of snow is within the first 11 you sample.

geomcdf(p=.1, p=11)

300

There is a 10% chance of snow on a given day in December. Find the probability that you sample more than 15 days before you the first day of snow.

1-geomcdf(p=.1, p=15)

400

There is a 15% chance of someone having red hair.  What is the mean number of people you would need to sample to find the first person with red hair?

1/.15 = 6.67

500

There is a 10% chance of snow on a given day in December. Find the probability that the first day of snow either the 7th or 9th day you sample.

geompdf(p=.1, r=7)+geompdf(p=.1, r=9)

Normal Approximation

100

What is the formula for mean of the binomial?

mu=np

200

What is the standard deviation of the binomial distribution?

sigma = root^(np(1-p))

300

To be normal, what is the requirement for np and n(1-p)?

>=10

400

What is the z-score for the 20th percentile?

z = -0.84

500

What are the z-scores for the cutoffs for the middle 66% of scores?

z = -0.95 and z = 0.95