Math Answers

1. Let S be the set of all strings of English letters. Determine whether these relations are reflexive, irreflexive, symmetric, antisymmetric, and/or transitive.

a) R1 = {(a, b) | a and b have no letters in common}

b) R2 = {(a, b) | a and b are not the same length}

c) R3 = {(a, b) | a is longer than b}

a. List the sample space in the given experiment. How many outcomes are

possible?

b. Construct a table showing the number of defective computers in each

outcome and assign this number to this outcome. What is the value of the

random variable X?

c. Illustrate a probability distribution. What is the probability value P(X) to

each value of the random variable?

d. What is the sum of the probabilities of all values of the random

variable?

e. What do you notice about the probability of each value of the random

variable?

Using payback, ARR, and NPV with unequal cash flows Medeiros Manufacturing, Inc. has a manufacturing machine that needs attention. The company is considering two options. Option 1 is to refurbish the current machine at a cost of $1,000,000. If refurbished, Medeiros expects the machine to last another 7 years and then have no residual value. Option 2 is to replace the machine at a cost of $2,000,000. A new machine would last 9 years and have no residual value. Medeiros expects the following net cash inflows from the two options:

Hint: The area of a circle is calculated as πr2. A square sheet of metal has sides 2p. The circle fits perfectly into the square:

Suppose the IQ of the learners in a certain University follows a normal distribution with

mean 110 and standard deviation 100?

a What proportion of the learners population have IQ's more than 90 but less than 100?

b. A random male learner is selected from this University. What is the chance that his IQ is more than 136?

c Stacy de leon, a Physics major, is prolific writer and a Math genius of this

university. If it is known that Stacy's IQ belongs to the upper 1% of the learner

population, what is her minimum IQ?

Independent Assessment 2

Four coins are toss. Let Y be the random variable representing the number of

tails that occur. Find the values of the random variable Y.

Possible Outcomes

Value of Random Variable Y

(number of tails)

 Four coins are tossed. Let Z be the random variable representing the number heads that occur. Find the values of the random variable Z. ( Take note that you should have 2 = 16 possible outcomes ).

A company manufactures soaps. The mean mass of the soaps is 300g with variance 52g. A sample of 100soaps was selected.

a)Find the probability of selecting soaps more than masses 320g.

b)How many soaps will have masses between 280g and 500g.

A company manufactures fuses. The percentage of non-defective fuses is 95.4%. A sample of 10 fuse was selected. Calculate the probability of selecting at least 3 defective fuses.

5. What is the probability that a market inspector will discover, greater than five violations of the public health code?