Math Answers

A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability0.10 of giving a (false) positive when applied to a non- sufferer. It is estimated that 0.5 % of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population). Calculate the following probabilities:

(a) that the test result will be positive.

(b) that, given a positive result, the person is a sufferer.

(c) that, given a negative result, the person is a non-sufferer.

The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2,…, 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on).

a. What is the probability that both selected setups are for laptop computers?

b. What is the probability that both selected setups are desktop machines?

c. What is the probability that at least one selected setup is for a desktop computer?

d. What is the probability that at least one computer of each type is chosen for setup?

a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit

can be used only once? (05)

(b) How many of these are odd numbers? (05)

(c) How many are greater than 330?

An employee of a big business company earns a gross annual salary of

₱450,000. What is the weekly, and monthly pay for this employee?

1. The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight?

Suppose that 𝑑𝐴 𝑑𝑡 = −0.0004332 𝐴(𝑡) represents a mathematical model for the radioactive decay of radium – 226, where 𝐴(𝑡) is the amount of radium (measured in grams) remaining at time 𝑡 (measured in years). How much of the radium sample remains at the time 𝑡 = −0.002 with initial condition 𝐴(1) = 0.005

Consider a flask that contain 3 liters of salt water. Suppose that water containing 25 grams per liters of salt is pumped into the flask at the rate of 2 liters per hour, and the mixture, being steadily stirred, is pumped out of the flask at the same rate. Find a differential equation satisfied by the amount of salt 𝑓(𝑡) in the flask at time 𝑡.

Aneco an Electrical Company claims that the average lifeof the bulbs it manufactures is 1,200 hours with a standard deviation of 250 hours. If random sample of 100 bulbs is chosen, what is the probability that the sample mean will be.

A sociologist believes that it costs more than P90,000 with a standard deviation of

P4,500 to raise a child from birth to age one. A random sample of 49 families, each with

a child is selected to see if this figure is correct. The average expenses for these families

reveal a mean of P92,000. Based on these sample data, can it be concluded that the

sociologist is correct in his claim? Use 0.05 level of significance.

Step:

1.State the null and alternative hypothesis

concerning the population mean, "\\mu" and the

type of test to be used

2. Specify the level of significance "\\alpha"

3. State the decision rule.

4. Collect the data and perform calculations.

5. Make a statistical decision.

6. State the conclusion.

Find out whether the following functions are one to one or not

(a) f(x)=3x+4 (b) f(x)=x²+4 (c) h(x)=13x⁵+5 (d) g(x)=x⁴+3 (e) p(x)=1/x+3 (f) f(x) =|2x+5|