1. A random variable X is normally distributed with a mean of 10 and a standard deviation of 3.

(a) Find P(X > 12)

(b) Find P(X ≤ 5)

(c) Find P(12 ≤ X < 20)

(d) Find b such that P(X > b) = 0.9782

2. A random variable X is normally distributed with a mean of 95 and a standard deviation of 12. If P(A < X < B) = 0.8592, find A and B such that A and B are symmetric about the mean.

3. The weights of a particular species of animal are normally distributed with a mean of 10 pounds and a standard deviation of 2 pounds. If a newborn animal of this species is in the 85th percentile, what is its weight?

4. How many days will it take for a sum of $500 to earn $85 interest if it is deposited into an account paying simple interest at the rate of 4% per year?

5. An account pays simple interest at an annual rate of 4.75%. If the account grows to $15,250 over a 9 month period, what was the original amount placed in the account?

6. The amount of money in an account paying interest that is compounded quarterly doubles over a twenty yearperiod. What is the annual interest rate?

7. How long will it take for $490 to grow to $900 if it is placed in an account that pays interest at 4.75%/year compounded monthly?

8. An account pays interest at 5.75%/year compounded continuously. How much will be in the account at the end of the period if $925 is invested for a 15 year period?

9. What is the effective rate of interest of an account that pays 5.75% per year compounded daily?

10. What is the effective rate of interest of an account if it pays interest compounded quarterly and $5,000 grows to$7,500 over a 9 year period?