Math Answers

A Telkom company bond carries an 8% coupon, paid semi-annually. The par

value is R1000, and the bond matures in six years. If the bond currently sells for

R911.37, what is its yield to maturity?

Suppose you have celebrated your 19th birthday. A rich uncle set up a trust fund

for you that will pay you R100 000 when you turn 25. If the relevant discount rate is

11 percent, how much is the fund worth today?

Assume the total cost of a tertiary education will be R75 000 when your child

enters university in 18 years. You presently have R7 000 to invest. What rate of

interest must you earn on your investment to cover the cost of your child’s tertiary

education?

2. Suppose that the average outstanding credit card balance for young professionals is

Php11,200 with standard deviation of Php 2,600. In simple random sample of 150 young

professionals, what is the probability that the mean outstanding credit card balance does

not exceeds Php12,300?

(HINT: Central Limit Theorem)

Use set builder notation to give a description of each of these sets. a) {0, 3, 6, 9, 12} b) {−3,−2,−1, 0, 1, 2, 3} c) {m, n, o, p}

Use Euler and modified Euler method with one step find the value of y at x=0.1 for given dy/dx=x^2 +y and y=0.94 when x=0

10. The length of time, in minutes, for an airplane to wait for clearance to take off at a certain

airport is a random variable Y = 3X − 2, where X has the density function

f(x) = {1/4^e−x/4, 0.

x > 0

elsewhere,

Find the mean and variance of the random variable Y.

9. The probability density function for a diameter of a drilled hole in millimeters is f(x) =

10e^−10(x−5)

for x > 5 mm. Although the target diameter is 5 mm, vibrations, tool wear,

and other nuisances produce diameters larger than 5 mm.

a) Determine the mean and variance of the diameter of the holes. [Hint: Use

integration by parts.]

b) Determine the probability that the hole exceeds 5.1 mm.

8. Suppose the probability density function of the length of computer cables is f(x) = 0.1

from 1200 to 1210 millimeters.

a) Determine the mean and standard deviation of the cable length.

b) If the length specifications are 1195 < x < 1205, what proportions of cables are

within specifications?