Math 201 Practice Exam I

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

Printable Key

Problem 1   Categorize these measurements associated with Lake Tahoe according to level:

nominal, ordinal, interval, or ratio.

1. The depth of clarity of the lake.

2. The time at which the first boat passes through from the Keys.

3. The type of fish that is the first to be caught in the morning.

Problem 2

You are interested in finding out the average number of classes that students take at LTCC.  Since you can't find out this information for every student, you have all instructors who teach at 10:00 AM to survey all of their classes.

A.  Is this a random sample?  Explain your reasoning.

B.  What type of sampling is this?

Problem 3

A.  You did research to determine the number of snow boarders who rode Sierra each Wednesday in January.  You came up with the following data.

 Week 1 2 3 4 No. of Boarders 800 600 400 900

Construct a time plot and a bar chart for this data.

Problem 4

You are interested in the distribution of tree size in the Lake Tahoe basin.  You take a random sample of 24 trees and measure their diameters (in inches).  Below is the data that you collected.

0    3    4    4    6    7    8    8    9    10    10    10   11    12    14

16   17   19    24    24    29    30    34    39

A.      Make a frequency table and histogram for this data.  Use 4 class intervals

Solution

B.      Make a Stem and Leaf Display of this data.

Solution

C.      Describe the distribution of the data using the language of statistics.

Solution

D.      If a 25th tree was found to have a diameter of 48 inches would the standard deviation increase or decrease.  (Answer this without calculating)

Solution

E.   In what percentile is the tree that has a diameter of 7 inches?

Solution

Problem 5

Twenty students were asked how far they travelled each day to get to the college.  Nineteen of the students all traveled between 0 and 7 miles, but one student lived in Sacramento and traveled 100 miles each day.

A.  Which of the following would be changed significantly if the student from Sacramento had not been surveyed:  mean, median, mode, standard deviation, variance, 5% trimmed mean?

B.  Suppose that the student from Sacramento had not been surveyed and that the mean was calculated to be 3.2 and the standard deviation was 0.9.  Use a sentence or two to interpret the standard deviation  in the context of the study.

Solution

Problem 6

Last year, 2,000,000 Kokanee Salmon hatched in Taylor Creek.  Of those, only 20,000 reached to one year.  12,000 of the survivors were female.

A.  What is the estimated probability that a hatched egg will live for at least one year?

Solution

B.  What is the estimated probability that a Kokanee that lives to one year will be female?

Solution

C.  What is the estimated probability that a hatched egg will live for at least one year and will be female?

Solution

D.  Estimate the probability that a hatched egg will die before it reaches one year old?

Problem 7

You roll two fair six sided dice.

A.  What is the probability that the sum of the two dice is four?

Solution

B.  What is the probability that the sum of the two dice is a nine given that the first die was a six?

Solution

C.  What is the probability that the sum of the two dice is larger than 3?

Problem 8

In your collection of nine pens you know that three are out of ink.  Since you are in a rush to get to your midterm, you randomly select two of the pens (a blue one and a black one).

A.  Draw a tree diagram for the outcomes of this experiment.  Show the probabilities of each stage on the appropriate branch.

B.  Use the tree diagram to determine that probability that at exactly one of the pens is not out of ink.

Problem 9

Determine the probability of getting a Royal Flush in Poker (5 card stud).  (Recall that a Royal Flush is Ace King Queen Jack and Ten all in the same suit.  Also recall that there are 52 cards in a deck and a poker hand has five cards.

Problem 10

You are the manager of the chicken and steak house restaurant which has two items on the menu:  the chicken dinner and the steak dinner.  30% of your customers order steak.  If you have 15 customers this evening, what is the probability that exactly 5 of them will order steak?

Extra Credit:  Write down one thing that your instructor can do to make the class better and one thing that you feel that the instructor should continue doing.

(Any constructive remarks will be worth full credit.)