MATH533 â Final Exam

Worksheet

Given the following sample of 10 high

temperatures from March: 55, 60, 57, 43,

59, 66, 72, 65, 59, 47.

Determine

the mean.Determine the median.Determine the mode.Describe the shape of the distribution.Determine Q1, Q2, Q3 and IQR.

The contingency table shows classification of

students in a Statistics class.

From NJ

From PA

GPA at least 3.0

15

5

20

GPA below 3.0

45

35

80

60

40

100

If a student is selected at random, what is the

probability that he/she is from NJ?If a student is selected at random, what is the

probability that he/she has a GPA below 3.0?If we know that the student is from PA, what is

the probability that he/she has a GPA of at least 3.0?If a student is selected at random, what is the

probability that he/she is from NJ and has a GPA below 3.0.If a student is selected at random, what is the

probability that he/she from PA and has GPA of at least 3.0.

Your friend is applying for 4 jobs. The hourly pay rate for the 4 jobs are, $8,

$12, $15, $20. The probability

distribution below shows the probability of getting each of these jobs:

Job

Pay Rate, X

Probability,

P(X)

8

.30

12

.20

15

.40

20

.10

What is the probability that your friend will

get a job paying at least $15/hour?What is the expected pay rate for your friend?

It is known that 31% of cars are considered gas

hogs (i.e. they give less than 15 mpg).

If we select 20 cars at random:What is the probability that exactly 4 will be

gas hogs?What is the probability the at least 4 but not

more than 7 will be gas hogs?How many cars are most likely to be gas hogs?You ask all 200 students at school how much

money they have in their pockets. The

amount ranges from $0 to $130. You determine

the mean to be $56.40 with standard deviation of $8.40. You believe that the amount is normally

distributed.If you pick a person at random, what is the

probability that he/she has at least $45?What percentage of the students will have

between $40 and $50 in their pockets.If you pick a person at random, what is the

probability that he/she has either less than $30 or more than $70.Approximately how many people in the class do

you expect to have at least $65?We want to identify the students with top 10.5%

amounts as ârichâ. What is the minimum

dollar amount the students in this group would need in their pockets.Assume that on the third exam in a calculus

course, the average score over the years has been 72 with a standard deviation

12. You are currently taking the course

and there are 25 students in the class?

What is the probability that

the mean score for your class will be greater than 75?

What is the probability that

the mean score for your class will be between 68 and 70?

A sample of 25 days in summer yields an average

high temperature of 80 with a standard deviation of 12.Give a point estimate of the true mean of the

high temperature.Find a 99% confidence interval for the average

high temperature for the summer.How big a sample do we need if we want to be 90%

confident of being within 7 degrees of the population mean?A sample of 100 exams yielded an average grade

of 82 and standard deviation of 14. Find

a 95% confidence interval for the average exam grade.Heights of aliens from Mars are known to be

normally distributed with a population standard deviation of 9 inches. How big a sample do we need to take if we

want be 95% confident that our error will not exceed 3 inches?Preliminary studies have shown that 20% of the

voters might be willing to vote for Sran for President. Construct a 90% confidence interval for the

proportion of voters who would be willing to support Sran.Before entering the race, Sran would like to conduct

a poll to check his level of support. How

big should be the sample be if he wants to be 95% sure that the error is no

more than 2%?The average weight of men joining a gym has

historically been 170 pounds with a standard deviation of 27. The owner feels that the average weight has

now decreased to less than 165 pounds.

To support his claim, the owner conducts a sample of 25 men and finds

their average to be 153. He would like

to use a significance level of .05 to test his claim.State the null hypothesis.State the alternate hypothesis.Will you use z or t distribution for this

problem?Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.Determine the critical value.Determine the rejection region.Calculate the test statistic.Would you accept or reject the ownerâs

claim? Explain.The average score on a certain college entrance

test has been known to be 240. The dean

of a university feels that this has changed.

He conducts a sample of 25 students to test his claim. The sample yields an average of 232 with a

standard deviation of 25. He would like to use a significance level of .10.State the null hypothesis.State the alternate hypothesis.Will you use z or t distribution for this

problem?Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.Determine the critical value.Determine the rejection region.Calculate the test statistic.Would you accept or reject the deanâs claim?A presidential candidate states that she

currently has exactly 30% of the vote. A

newspaper thinks that this number is inaccurate. So it conducts a sample 500 voters and finds 175

people support the candidate. The

newspaper would like to test its claim using .05 significance level.State the null hypothesis.State the alternate hypothesis.Will you use z or t distribution for this

problem?Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.Determine the critical value.Determine the rejection region.Calculate the test statistic.Would you accept or reject the newspaperâs

claim?

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