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

Fall 2013 - Math 141 Daily Grade 13A

Take-Home Assignment over Sections 8.5/8.6 and 5.1 Due at the beginning of class on ***Tuesday***, November 26, 2013

Name: Seat#: Section: 501 507

You must show ALL of your work to receive full credit. Please write neatly and clearly box in your final answers. Round your answers to

the nearest penny (if dealing with dollars). Otherwise, round your answers to four decimal places. If the calculator is used for anything

other than arithmetic, you must tell me what was entered into the calculator, what function was used, and what the calculator returned to

you. You are allowed to work together but copying will not be tolerated. I will ask you to pass in the assignment (in seat order) as soon as

class begins. If you walk in late, please bring the assignment to the front. This assignment will only be accepted if it is placed on the table

at the front of the classroom before 10 minutes of class have passed. Otherwise, no credit will be given.

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 year period. 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?

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