Homework Answers

An auto battery company claims that their batteries' mean life is 50 months. In order to check this cla, a DTI researcher took a random sample 18 of these batteries and found that the mean life is 48.8 months with standard deviation of 7 months. Aasume the battery life follows a normal destribution, test with 90% confidence wether the companies'claim is different from the true mean.

In a survey of 120 professors, a research found that 50 preferred traditional method of teaching, 78

preferred computer-aided method, and 66 preferred group method. In addition, 36 preferred any of

the two methods of teaching and 24 professors preferred them all.

a. Find the number of professors who prefer at least one of the teaching methodologies

b. Find the number of professors who do not prefer any of the teaching methodology

Let A = {1, 2, 3, 4}, B = {3, 4, 5, 6, 7}, C = {2, 3, 8, 9}. Perform the following

a.

𝐴∪𝐵

b.

𝐴∩𝐵

c.

𝐴∪𝐶

d.

𝐴∩𝐶

1. The mean lifetime of a sample of 100 light bulbs produced by a certain company is found to be 1580 hours. Test the hypothesis at 5% level of significance that the mean lifetime of the light bulbs produced by the company is 1,600 hours with sd of 90 hours.

I have 6 colors which is Blue, Red, Yellow, Orange, And Green and each of them is equal to each other, so now what is the propability that i will get red?

Proof using Osborne's rule that 1-tanh^2x=Sech^2x

Proof using Osborne's rule that cosh2A=Cosh^2A+Sinh^2A

Use a Venn Diagram to illustrate the following:

a. The subset of odd integers in the set of all positive integers not exceeding 10

b. The set of all months of the year whose names do not contain the letter R in the set of all months

of the year