Math Answers

A company has developed a new battery. The engineering department of the company claims that each battery lasts for 200 minutes. In order to test this claim, the company selects a random sample of 100 new batteries so that this sample has a mean of 190 minutes. Given that the population standard deviation is 30 minutes, test the engineering department’s claim that the new batteries run with an average of 200 minutes. Use 1% level of significance.

4)Given that the level of significance is 0.01 or 1%, what is/are the critical values?

5)Using the appropriate formula, what is the computed test statistic? (Input your answer using 3 decimal places, example: 1.234 if positive or -1.234 if the answer is negative) *

6)What is the decision based from the critical value and the computed test statistic

7)What is the conclusion?

A company has developed a new battery. The engineering department of the company claims that each battery lasts for 200 minutes. In order to test this claim, the company selects a random sample of 100 new batteries so that this sample has a mean of 190 minutes. Given that the population standard deviation is 30 minutes, test the engineering department’s claim that the new batteries run with an average of 200 minutes. Use 1% level of significance.

1)Which is the correct null hypothesis that can be derived in the situation?

2)Which is the correct alternative hypothesis that can be derived in the situation? 

3)What test will be used based from the given values in the situation?

A population consist of the number 2,3,4

a. Enumerate all possible sample size of 2.

b. Compute for the mean of each sample.

c. Find tye mean of the mean.

d. Find the standard deviation of the sample means.

e. Find the population mean.

f. Find standard deviation.

g. Find the standard error of the mean

u( x, y) = e^x(xsiny+ycosy) find the differentials

What's poison distribution

Sprinters who run races involving curves around a track (usually distances over 200 meters) often have a preference for a particular lane. A runner might feel that an assignment to an outside lane places her at a disadvantage relative to her opponents. In fact, a 2001 survey of college-level sprinters found that 75% preferred to run in lane #4.

Consider this experiment. As a race organizer, you randomly select five runners from a pool of nine and assign them to lane #1, lane #2, lane #3, and so on, in the order they are selected.

How many experimental outcomes are there for this experiment? 

Let X follows a normal distribution with mean 40 and variance 9. Then mean of Y= (X-40)/3 is

        [ 1 0 -1

3. Consider the matrix A =  0 3 0

                      -1 0 1 ]

1. Find the eigenvalues of A.
2. Find the eigenspaces corresponding to each eigenvalue from A.

2. Consider a linear transformation T: R³ → R³ defined by

  ([x         [ x + 4y +3z  

T  y     =      -5y - 4z 

    z])        5x + 10y + 7z ]

Note: T is a 3x1 matrix containing x, y, z respectively. T is equal to another matrix as shown above.

a) Find the matrix A for T

b) Find a basis for ker(T) and the dim(ker(T)). Then find dim(Im(T)), without finding a basis for Im(T). (Show all working)

c) Find a basis for Im(T)

1. Answer the following questions

                                                              →            →            →  [ 1

a) Consider the linear transformation T(x) = proj_u(x), where u =  0

                                                                                                      3 ] 

Find the matrix for T.

b) Find the matrix for the linear transformation which reflects every vector in R² across the x-axis and then rotates every vector through an angle of 𝝅/6. (Show all working)