Final Exam

NAME:________________________________

DATE:_________________________________

___________________MATH122–Final Exam

Question 1

You are going to make plans for the weekend. The weatherman informs you that

there is a 25% chance that it rains on Saturday, a 31% chance of rain on Sunday,

and a 12% chance that it rains on both days.

__A)_Find the probability that it does not rain on Saturday.

__B)_Find the probability that it rains on Saturday or Sunday.

__C)_Find the probability that it rains on Sunday given that it rains on Saturday.

__D)_Is the probability of rain occurring on Saturday independent of rain

_____occurring on Sunday? Explain.

Question 2 A professor is giving a final exam for the advanced statistics class. He has a bank

of thirteen possible questions, and he plans to ask five questions on the exam.

__A)_How many different orderings of the five random questions are possible?

__B)_How many different combinations of the five random questions are possible?

Question 3

Suppose an unfair die is rolled. Let random variable X indicate the number that the

die lands on when rolled taking on the following probability values.

x 1 2 3 4 5 6

Pr(X = x ) .05 .10 .20 .40 .15 .10

__A)_Find the probability of rolling a 2 or a 6.

__B)_Find the probability of rolling a number greater than 4.

__C)_Find the probability of not rolling a number less than or equal to 5.

__D)_Find the expected value of a die roll.

__E)_Find the variance of a die roll.

__F)_Find the standard deviation of a die roll.

Question 4 Imagine an experiment where a person is seated in front of a computer. When a

certain signal flashes on the screen, the subject presses a key on the keyboard as

quickly as possible. A clock measures the amount of time that elapses between the

signal’s appearance and the subject’s keypress. This amount of time is known as

the reaction time. Different subjects take different amounts of time to react to the

signal. Based on research, the experimenter believes that the reaction times have a

normal distribution with  = 200 milliseconds and σ = 25 milliseconds.

__A)_What percent of the subjects in the experiment should have reaction times of

_____ 228 milliseconds or less?

__B)_What percent should have reaction times between 185 and 246 milliseconds?

100 200 300

__C)_What percent of the subjects in the experiment should have reaction times

_____greater than 215 milliseconds?

__D)_Suppose a sample of 36 research participants are collect. Find the probability

_____that the sample average will be less than 196.

Question 5 The table of sample statistics below displays the fasting cholesterol level for

adolescent boys and girls during 2008.

Sample Data Boys Girls

Mean 225 213

Standard Deviation 15.3 14.9

Size 21 25

__A)_Give the 90% confidence interval for the population mean cholesterol

_____level of girls.

__B)_Give the 99% confidence interval for the population mean cholesterol

_____level of boys.