## Finite Math

### Dr. Wilson

1. Some members of a class took a test. The scores were summarized in the following frequency distribution. Find the mean median, mode, the upper and lower quartiles, and standard deviation of the scores, and draw the histogram.

 x | f 90 | 2 80 | 3 70 | 1 60 | 4

2. The mean high temperature in July for a town in the Central Valley is 106. If the standard deviation is 2 degrees, what is the probability that the temperature will not reach 100 on a given day?

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3. Linda took a multiple choice test. She did pretty well, but there were 5 questions where she had to guess. Each question had 4 choices for answers. Make up a probability distribution for the number of correct guesses. Find the mean and standard deviatiion. Draw the histogram. What is the probability that she got at least 2 right?

4. A fair die is rolled 150 times. What is the probability of a 6 coming up between 20 and 30 times? (20 times or 30 times would count.)

5. Linda puts \$100 in the bank getting 6% annual interest compounded monthly. If she leaves it there for 15 years, how much will it be worth?

6. Linda puts \$100 in the bank each month for 15 years. If the bank gives 6% annual interest compounded monthly, how much will she have after 15 years.

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7. Find the monthly payments on a \$100,000 30 year mortgage if the annual interest rate is 8.5% compounded monthly.

What would the monthly payments be for a 15 year mortgage at the same interest rates?

8. The following is a table of homework averages and final course grades for selected students from a Finite Math class.

 HW CG 96 94 100 98 78 83 60 65 92 85

Find the line of best least squares fit for predicting the final average in the course as a function of the homework grade. What kind of a final average would this model predict for a person who got a 90 for their homework average. Compute Pearson's   r.   What does Pearson's   r   tell us about these distributions?

9. Suppose you win \$30 million in the lottery. The state wants to spread the payments out over 20 years, to which you agree for tax reasons. How much will the state have to put into an interest bearing account getting 7% annual interest in order to pay you \$1.5 million per year for the next 20 years and have no money left in the account after the end of the 20 years?

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