In Class Exam 3 Review Math 166

1. Classify each random variable as continuous, infinite discrete or finite.

A coin is randomly selected from a box of coins containing nickels, dimes, quarters and pennies. Then the coin is returned to the box.

a) X is the money value of the coin.

b) Y is the un-rounded weight of the person choosing the coin.

c) N is the number of times a coin must be selected until a nickel is chosen.

2. A box contains 10 red, 6 blue and 4 green balls. Three are randomly selected without replacement. X= the number of green balls chosen.

Write the distribution of X and find E(X).

3. a) The heights in inches of 5 4^th -graders are 50, 52, 51.5, 57 and 54. Find the mean, median, mode and standard deviation of their heights.

b) The heights of 20 4^th-graders rounded to the nearest inch are shown in the table.

Height 50 51 52 53 54 55 56 57

# students 1 3 4 2 5 2 2 1

Find the mean, median, mode and st.dev. of their heights.

4. Scores on two 5-point quizzes are shown.

Score 0 1 2 3 4 5

Quiz 1 2 3 5 5 3 2

Quiz 2 5 3 2 2 3 5

Which quiz has higher standard deviation of scores and why?

5. I A person draws one card from a standard 52-card deck.

a) What are the odds he will select an ace?

b) What are the odds he will not select an ace?

II If the odds in favor of E are 2:9, find P(E).

6. Classify each random variable as binomial or not. If binomial, give n, p, the mean and the standard deviation. If not binomial, say why not.

a) A shipment contains 100 games, two of which are defective. 10 games are selected at random and X is the number of defective games.

b) Games are continually produced so that 2% are defective. A sample of 10 games are selected at random and X is the number of defective games.

c) 1/3 of the population has blood type A+. Fifty people are selected at random and X is the number who have blood type A+.

d) A box contains 10 red, 6 blue and 4 green balls. Three are randomly selected without replacement. X= the number of green balls chosen.

7. Assume that 6% of a large population has a non-communicable disease. 500 people are randomly selected and X is the number of those selected who have the disease.

a) Find P(X=30)

b) Find P(20<X<30).

c) Find the normal approximation to the probability in b.

8. X is a normally distributed random variable with mean 30 and unknown standard deviation.

P(X>25)=0.8. Find

a) P(X<35) b) P(X>35) c) P(25<X<30)

9. A set of grades is normally distributed with mean 70 and standard deviation 16.

i) Find a number a so that 60% of the grades are below a.

ii) Find a number b so that 15% of the grades are above b.

iii) Find P(X<80) where X is a randomly selected student’s grade.

10. Assume money earns the annual rate of 8% simple interest.

a) Find the accumulated amount after 10 years if the initial amount is $1500.

b) Find the initial investment amount if the accumulated amount after 10 years is $4500.

11. Find the effective rate of annual interest rate 7% compounded

a) quarterly. b) monthly. c) daily.

12. A person makes a $60000 down payment on a $200,000 house. The rest is financed at 6.5% annual interest compounded monthly. The loan is to be paid off in 30 years.

a) Find the monthly payment.

b) How much is still owed after 10 years?

c) How much of the 121^st payment is interest?

d) If the loan is refinanced after 10 years at annual interest rate 5% compounded monthly, what is their new payment?

13. How much should be deposited today at 5% compounded monthly to be able to withdraw $600 per month for 5 years starting 10 years from now? Assume money not yet withdrawn earns 5% compounded monthly.