Probability and Statistics Final

Probability

100

A bag contains 4 red marbles, 2 blue marbles, and 8 green marbles. What is the probability of selecting a red marble?

4/14

200

A bag contains 4 red marbles, 2 blue marbles, and 8 green marbles. What is the probability of selecting a red or a green marble?

12/14

300

A bag contains 4 red marbles, 2 blue marbles, and 8 green marbles. What is the probability of selecting a red marble on the first pick and then a blue marble?

4/14 x 2/13 = 8/182

400

Holly is going to draw two cards from a standard deck without replacement (she is not going to put the cards back). What is the probability that the first card is a king and the second card in an ace?

4/52 x 4/51 = 16/2652

500

If you flip a coin twice, what is the probability of flipping two tails. (Hint: Draw a tree diagram)

1/4

Permutations and Combinations

100

How many different ways can 3 people sit in a row at a movie theater?

3! = 6

200

You and 5 friends go bowling, how many different orders can you bowl in?

6! = 720

300

If 10 people run a race, how many different ways can they finish in first, second, and third place?

720

400

How may different 5 person teams can be created from a classroom of 13 students?

1287

500

20 people were trying to be one of the first 5 callers to a radio station. How many different sets of people could have succeeded?

15,504

Normal Distribution

100

Calculate the standard deviation and variance of the following data set. 5, 3, 4, 3, 7

s = 2 v = 4

200

Calculate the standard deviation and variance of the following data set. 10, 34, 44, 23, 17

s = 14 v = 196

300

In the United States, the average IQ is 110, with a standard deviation of 12. What percentage of the population would you expect to have an IQ lower than 100?

z = -0.83 p =.2033 = 20.33%

400

In the United States, the average IQ is 110, with a standard deviation of 12. What percentage of the population would you expect to have an IQ higher than 125?

z = 1.25 p= 1-.8944 = .1045 = 10.45%

500

In the United States, the average IQ is 110, with a standard deviation of 12. What percentage of the population would you expect to have an IQ between 105 and 150?

z = -0.42 z = 3.33 p = .9996 - .3372 = .6624 = 66.24%

Z-Scores

100

Use table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is representative of the answer to the question. z < 1.35

p = .9115 = 91.15%

200

Use table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is representative of the answer to the question. z > -1.67

p = 1 - .0475 = .9525 = 95.25%

300

Use table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is representative of the answer to the question. -0.95 < z < 2.45

.9929 - .1711 = .8218 = 82.18%

400

Use Table A to find the value of z of a standard normal variable that satisfies each of the following conditions. Be sure to use the value of z that is closest to satisfying the condition. In each case, sketch a standard normal curve with your value of z marked on the axis. The value of z with 15% of the observations falling below it?

.15 .1492 z = -1.04

500

Use Table A to find the value of z of a standard normal variable that satisfies each of the following conditions. Be sure to use the value of z that is closest to satisfying the condition. In each case, sketch a standard normal curve with your value of z marked on the axis. The value of z with 60% of the observations falling above it?

1 - .60 = .40 .4013 z = -0.25

Central Limit Theorem

100

Identify the following as statistics or parameters and explain your answer choice. Of all the teachers at H.D. Woodson, 25% take the bus to work in the morning.

Parameter

200

Identify the following as statistics or parameters and explain your answer choice. Of the 1,250 people in DC that were polled, 23% said that the museum of natural history was their favorite museum.

Statistic

300

The population has a mean of 24 and a standard deviation of 2. a.What is the mean of the sample? b.What is the sample standard deviation for a group N = 10 c.How large of a sample is needed to reduce the sample standard deviation to 1.5?

a. M = 24 b. s = 0.63 c. n = 1.77

400

You survey all students at H.D. Woodson on how many times a week they go to McDonalds. The mean number of trips to McDonalds students took to was μ = 2.1 with a standard deviation of σ = 0.5. If you take a sample of 25 students, what is the probability that group of students will take more than 2 trips to McDonalds?

s = 0.1 z = -1.00 p = 1 - .8413 = .1587 = 15.97%

500

A class of students took an English test. The results were normally distributed with a mean of μ = 73 and a standard deviation of σ = 11. What is the probability that a sample group of 36 students scored below a 70?

s = 1.83 z = -1.64 p = .0505 = 5.05%