Question 1

Decide if each distribution below represents a valid probability distribution. (a)

x	P(x)
0	0.16
1	0.35
2	0.32
3	0.15
4	0.03
5	0

Sum of the probabilities = Because the sum of the probabilities Select an answer is is not equal to 1, this Select an answer is not is a valid probability distribution. (b)

x	P(x)
0	0.04
1	0.19
2	0.33
3	0.29
4	0.13
5	0.02

Sum of the probabilities = Because the sum of the probabilities Select an answer is is not equal to 1, this Select an answer is is not a valid probability distribution.

Question 2

x	P(x)
0	0.05
1	0.15
2	0.2
3	0.6

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

Question 3

Find the mean, , of this probability distribution.

X	P(x)
0	0.25
1	0.1
2	0.2
3	0.45

u =........... (Please show your answer to one decimal place.)

Question 4 Find the standard deviation, q, of this probability distribution.

X	P(X)
0	0.2
1	0.3
2	0.25
3	0.25

q = (Please show your answer to 1 decimal place.)

Question 5

In the following probability distribution, the random variableXrepresents the number of activities a parent of a 6th-8th grade student is involved in.

X	0	1	2	3	4
P(X)	0.05	0.105	0.237	0.303	0.305

a) Compute and the mean of the random variableX.

b) Compute the variance of the random variableX.

c) Compute the standard deviationof the random variableX .

d) What is the probability that a randomly selected student has a parent involved in 3 activities?

Question 6

Complete the following probability distribution table:

X	P(X)
-24	0.14
-1	0.18
77	0.2
83
84	0.22

Question 7

Suppose that the random variable x, shown below, represents the number of speeding tickets a person received in a three-year period. P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions.

x	P(x)
0	0.6121
1	0.1904
2	0.073
3	0.0623
4	0.032
5	0.0302
6+	0.0000

a) What is the probability that a randomly selected person has received four tickets in a three-year period? P(x=4)= b) What is the probability that a randomly selected person has received four or more tickets in a three-year period? P(x4)= c) What is the probability that a randomly selected person has received more than four tickets in a three-year period? P(x>4)= d) Would it be unusual to randomly select a person who has received four tickets in a three-year period?

• Yes
• No

Question 8

Suppose that the random variable x, shown below, represents the number times . P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions. 27

x	P(x)
0	0.3571
1	0.2624
2	0.2397
3	0.057
4	0.0427
5	0.0411
6+	0.0000

a) What is the probability that a randomly selected person has received two tickets in a three-year period? P(x=2)= b) What is the probability that a randomly selected person has received three tickets in a three-year period? P(x=3)= c) What is the probability that that a randomly selected person has received more than three tickets in a three-year period? P(x>3)= d) What is the probability that that a randomly selected person has received two or less tickets in a three-year period? P(x2)=

Question 9

A large fast-food restaurant is having a promotional game where game pieces can be found on various products. Customers can win food or cash prizes. According to the company, the probability of winning a prize (large or small) with any eligible purchase is 0.1. Consider your next 20 purchases that produce a game piece. Calculate the following: (Give answers to 4 decimal places.)

a) What is the probability that you win 4 prizes?

b) What is the probability that you win more than 5 prizes?

c) What is the probability that you win between 3 and 5 (inclusive) prizes?

d) What is the probability that you win 3 prizes or fewer?

Question 10

It is estimated that 48.4% of Kickstarter projects are successfully funded. Assume each Kickstarter project is independent. A random sample of 15 Kickstarter projects are followed. Let X be the number Kickstarter projects that are successfully funded. Calculate the following:

a. PX:

b. PX:

c. P(X=7):

d. P(X<9):

e. P(X>6):

f. P(X6):

g. P(6X9):

Please answer the questions sequentially. Thanks