Analysing the Statistical Analysis

¶ … die is rolled. What is the probability that the number on top is the following?

Three can only come about once. Since the chances can be six, the probability is 1/6.

An odd number

There are three odd numbers, which are 1, 3, and 5. Therefore probability is 1/6 + 1/6 + 1/6 = 3/6

A number less than

There are four numbers less than five, which are 1, 2, 3 and 4

Therefore, the probability is 1/6 + 1/6 + 1/6 + 1/6 = 4/6

A number greater than

There are three numbers greater than 3, which are 4, 5, and 6. Therefore the probability is 1/6 + 1/6 + 1/6 = 3/6

What are the odds in favor of a high school female athlete being drafted by a pro-basketball team?

What are the odds against a female basketball player who makes a freshman college roster playing as a senior?

4,313

c. What is the probability of a high school female athlete being drafted by a pro-basketball team?

/ (452,929 + 1)

= 1 / 452,930

d. What is the probability of a NCAA senior female athlete being drafted by a pro-basketball team?

Odds = 1

Therefore, probability = 1 / 32 +1

= 1/33

Problem 4.16

One dog 63/100

Dog owner 1/2

More than one dog 37/100

Not a dog owner 1/2

1/2 * 63/100 = 63/200

Problem 4.28

Determine whether each of the following pairs of events is mutually exclusive.

a. Five coins are tossed: "one head is observed," "at least one head is observed."

Mutually exclusive

b. A salesperson calls on a client and makes a sale: "the sale exceeds $100," "the sale exceeds $1,000."

Mutually exclusive

c. One student is selected at random from a student body: the person selected is "male," the person selected is "older than 21 years of age."

Mutually exclusive

d. Two dice are rolled: the total showing is "less than 7," the total showing is "more than 9."

Not mutually exclusive

Problem 4.36

Determine whether each of the following pairs of events is independent:

a. Rolling a pair of dice and observing a "1" on the first die and a "1" on the second die

Independent

b. Drawing a "spade" from a standard playing cards deck and then taking another "spade" from the very same pack without swapping the initial card

Independent

c. Same as part (b), except the first card is returned to the deck before the second drawing

Not independent

d. Owning a red automobile and having blonde hair e. Owning a red automobile and having a flat tire today

Independent

e. Studying for an exam and passing the exam

Not independent

Problem 5.2

a. The variables in problem 5.1 are either discrete or continuous. Which are they and why?

i. Number of siblings -- continuous. This is because the number of siblings cannot change at the moment

ii. Number of conversations -- discrete. There will be more conversations to be held between the children and the mothers.

b. Explain why the variable "number of dinner guests for Thanksgiving dinner" is discrete.

The variable is discrete because the number of guests can change through cancelation or extra invites.

c. Explain why the variable "number of miles to your grandmother's house" is continuous.

The variable is continuous because the distance cannot be change and the house will not move as it is stationary.

Problem 5.8

a. Express P open parenthesis x close parenthesis equals 1 over 6; for x = 1, 2, 3, 4, 5, 6, in distribution form.

P (1) = 1/6

P (2) = 2/6 = 1/3

P (3) = 3/6 = 1/2

P (4) = 4/6 = 2/3

P (5) = 5/6

P (6) = 6/6

b. Construct a histogram of the probability distribution P open parenthesis x close parenthesis equals 1 over 6; for x = 1, 2, 3, 4, 5, 6.

x

P (x)

10

0.4

11

0.2

12

0.2

13

0.1

14

0.1

60

1

c. Describe the shape of the histogram in part (b).

The shape of the histogram above is a probability histogram

Problem 5.18

Find the mean and standard deviation of the number of ships that arrive at a harbor on a given day

x

P (x)

xP (x)

x2

x2 P (x)

10

0.4

4

40

11

0.2

2.2

24.2

12

0.2

2.4

28.8

13

0.1

1.3

16.9

14

0.1

1.2

19.6

60

1

11.1

Mean = ? = ?[xP (x)] = 11.1

Variance = 129.5 -- (11.1)2 = 6.29

Standard Deviation = ?6.29 = 2.508