Statistics and Probability Answers

The director of an insurance company’s computing center estimates that the company’s computer has a 20% chance of catching a computer virus. However, she feels that there is only a 6% chance of the computer’s catching a virus that will completely disable its operating system. If the company’s computer should catch a virus, what is the probability that the operating system will be completely disabled?

1. A jeepney driver claims that his average monthly income is Php 3000.00 with a standard deviation

of Php 300.00. A sample of 30 jeepney drivers were surveyed and found that their average monthly 

income is Php 3500.00 with a standard deviation of Php 350.00. Test the hypothesis at 1% level of 

significance

I. Derive the mean and variance of a uniformly distributed random variable X where X ~ U (a, b). 

II. Let X be uniformly distributed in -2 ≤ x ≤ 2 Find:

a) P(X < 1)

b) P( X - 1 ≥ 1/2 ).

Dan works in an insurance company. Last January, he was able to insure 3 persons. Last February, he was able to insure 8 persons. Last March, he was able to insure 10 persons. Last April, he was able to insure 15 persons. Assume that the samples of size are randomly selected without replacement. Find the following:

a. The population mean

b. The population variance

c. The population standard deviation

d. The mean of the sampling distribution of means

e. The standard deviation of the sampling distribution of the sample means

Assume that the probability of a male birth is 1/2. Find the probability that in a family of 4 children there will be:

a) at least 1 boy and at least 1 girl. 

A random variable X is gamma distributed with α = 3, β = 2. Find: P(l ≤ X ≤ 2)

The time in hours a transistor lasts follows an exponential distribution with a mean of 100. Find the probability that a transistor lasts longer than

a) 15 hours.

b) 110 hours

c) 110 hours given that it lasts longer than 95 hours.

Determine the location and values of the absolute maximum and absolute minimum for the given function: 𝑓(𝑥) = (−𝑥 + 2) ସ , 𝑤ℎ𝑒𝑟𝑒 0 ≤ 𝑥 ≤ 3

Two extrusion machines that manufacture polyester fibers are being compared. in a sample of 1000 fibers taken from machine 1, 960 met specifications regarding fineness and strength. in a sample of 600 fibers taken from machine 2, 582 met the specifications. machine 2 is more expensive to run, so it is decided that machine 1 will be used unless it can be convincingly shown that machine 2 produces a larger proportion of fibers meeting specifications.

a. state the appropriate null and alternate hypothesis for making decision as to which machine to use.

b. compute the test statistics.

c. which machine should be used?