In a recent year, the scores for the reading portion of a test were normally distributed, with a mean oi 20.4 and a standard deviation of 5.5. Complete parts (a)through (d) below. (a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 13. The probability ot a student scoring less than 18 is :|.(Round to tour decimal places as needed.) (b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 13.5 and 27.3. The probability ot a student scoring between 13.5 and 2?.3 is D.(Round to four decimal places as needed.) (c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 31.7. The probability ot a student scoring more than 31.? is D.(Round to tour decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. 0 A. The event in part {a} is unusual because its probability is less than [1.115. O B. The event in part (c) is unusual because its probability is less than 11.05. C) C. None of the events are unusual because all the probabilities are greater than 0.05. O D. The events in parts {a} and (b) are unusual because its probabilities are less than 0.05.

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"

A. In a recent trading session, the benchmark 30-year Treasury bond’s market price went up A1 dollars per $1000 face value to A2 dollars, while its yield fell from .07 to .068. The bond’s market price then went up another A3 dollars per $1000 face value as the yield fell further to .0665 from .068. Report answers for the following (using average of latest two bond prices for duration and average of latest three bond prices for convexity):

1. Convexity, using the average of all three market prices of the bond in the denominator of the formula.

2. First modified duration, using average of first two market prices of the bond in the denominator of the formula.

3. Second modified duration, using average of second and third prices of the bond.

4. The expected rise in bond price if the interest rate were to fall another 20 basis points (.002) from .0665, using the average of two modified durations and convexity.

B. Estimate term structure of discount factors, spot rates and forward rates by using data on five semi-annual coupon paying bonds with $100 face value each: The bonds, respectively, have 1.25, 5.35, 10.4, 15.15 and 20.2 years to maturity; pay coupon at annual rates of B1, B2, B3, B4, and B5 percent of face value; and are trading at quoted spot market prices in dollars of B6, B7, B8, B9 and B10. Specify the discount factor function d(t) by a third degree polynomial with unknown parameters a, b, and c, as done in class. Using estimated d(t) function, determine spot rate and forward rate functions by assuming half-year compounding. Then write the values of the following based on your estimation.

5. Coefficient of parameter a in first bond price equation.

6. Coefficient of parameter b in first bond price equation.

7. Coefficient of parameter c in first bond price equation.

8. Coefficient of parameter a in second bond price equation.

9. Coefficient of parameter b in second bond price equation.

10.Coefficient of parameter c in second bond price equation.

11.Coefficient of parameter a in third bond price equation.

12.Coefficient of parameter b in third bond price equation.

13.Coefficient of parameter c in third bond price equation.

14.Coefficient of parameter a in fourth bond price equation.

15.Coefficient of parameter b in fourth bond price equation.

16.Coefficient of parameter c in fourth bond price equation.

17.Coefficient of parameter a in fifth bond price equation. 1

18.Coefficient of parameter b in fifth bond price equation.

19.Coefficient of parameter c in fifth bond price equation.

20.Parameter a.

21.Parameter b.

22.Parameter c.

23.Current price of a dollar at 5th year.

24.Current price of a dollar at 7th year.

25.Current price of a dollar at 10th year.

26.Current price of a dollar at 15th year.

27.Spot rate for term 2 year.

28.Spot rate for term 5 year.

29.Spot rate for term 10 year.

30.Spot rate for term 17 year.

31.Forward rate for half year period 2.5 to 3.0 years.

32.Forward rate for half year period 5.5 to 6.0 years.

33.Forward rate for half year period 10.5 to 11.0 years.

34.Forward rate for half year period 15.5 to 16.0 years.

C. Estimate the 2-year, 5-year, and 10-year key rate durations of a 20-year bond carrying a coupon of C1 percent on face value $100 paid semi-annually. The given term structure starts with C2 percent spot rate of interest at time zero and rises at a rate of 0.002 (.2%) per half year thereafter. Take a 20 basis point (.002) move in each key interest rate to calculate the key rate durations by the method done in class and given in textbook. Report answers for the following:

35. Current fair price of the bond with the given term structure.

36. Price change needed to calculate 2-year key rate duration.

37. Price change needed to calculate 5-year key rate duration.

38. Price change needed to calculate 10-year key rate duration.

39. 2-year key rate duration.

40. 5-year key rate duration.

41. 10-year key rate duration.

This assignment due 3 hours later …

• Attachment 1
• Attachment 2

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"

In a sample of 8 high school students, they spent an average of 28.8 hours each week doing sports with a sample standard deviation of 3.2 hours. Find the 95% confidence interval, assuming the times are normally distributed.

(26.12, 31.48)

(22.47, 35.21)

(25.62, 32.48)

(24.10, 34.50)

In a sample of 15 stuffed animals, you find that they weigh an average of 8.56 ounces with a sample standard deviation of 0.07 ounces. Find the 92% confidence interval, assuming the times are normally distributed.

(8.543, 8.577)

(8.528, 8.591)

(8.526, 8.594)

(8.521, 8.599)

Market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.7 million. If this estimate was based on a sample of 10 customers from a normally distributed data set, what would be the 90% confidence interval?

(3.06, 4.54)

 (2.81, 4.79)

(2.76, 4.84)

(2.11, 5.56)

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"

In a sample of 50,000 first-born babies, five were found to have Prader- Willie Syndrome. Determine the empirical probability that a families first child will be born with this syndrome.

50000/5=P(E)

P(A)= 0

P(A’) = 1

Sec. 11.5 #42

If a pointer is spun twice. Determine the probability that the pointer lands on:

• Red both times

2/6

• ask a question about your classmate’s solution
  • offer help when you see an error
  • seek help in completing your own problems

Note that only substantive postings will receive credit; nonsubstantive postings such as (but not limited to) “Good job!” or “Nice work!” will earn no credit.

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"