Math Answers

A random of 25 sample is drawn from a population with sample mean 105.2 and standard deviation 11.13 Construct a 90% confidence interval. *

Provide step-by-step solutions to the given problem below. Write your answers on

the spaces provided.

Consider all samples of size 2 from the population 2, 5, 6, 9, 11, and 13. Compute

the mean, and variance of the sampling distribution of the sample mean.

First step:

Second step

a)

b)

Third step

Fourth step

Fifth step

Sixth step

a)

b)

Seventh step

a)

b)

c)

d)

by using squeeze theorem shaw that the lim of 1-coax/x² =0 as x tends to 0

If the sample mean is 75 and the sample standard deviation is 5.Find the corresponding standard deviation of the score 70

Use formula to find z score z=x–x/ó

Use the Standard normal Curve to answer the following,On the first periodic exam in statistics,the population mean was 70 and the standard deviation was 9.Determine the standard score of the student who got a score of 88 assuming the score was normally distributed.

There are other geometries. One such is spherical geometry.

What can you say about the sum of the interior angles of a triangle in spherical geometry?

This question is concerning the completion of the square by using plane geometry

The area of a

The area of a rectangle of sides x and y is : xy

Consider the expression : x

2 + 10x

Such can be considered as the sum of two areas viz square x

2 and a rectangle 10x

Now do the following (sketch essential)

Divide the rectangle into two equal areas viz 5x and 5x

Next to the square place the two rectangles with the side x in common. One to the RHS and the other below.

You will now have a ’nearly complete’ square

a) What is the length of each side of the ’missing square’ in your diagram

b) If you add the area of the missing square to make a big square, what is the area of the complete (big) square

c) By using the areas from your sketch, find the expressions ? and ?? in the following:

x

2 + 10x + (?)2 = (??)2

Consider a population which is normally distributed.If the variance of the population is 9 and n=9,what is the variance of the sampling distribution of sample means

 A line up for tickets to a local concert had an average (mean) waiting time of 20 minutes with a  standard deviation of 4 minutes. 

a. What percentage of the people in line waited for more than 20 minutes? 

Obtain the solution of the differential equation

(x^2)y" - 2xy' + 2y = (log (base e) x) ^2, (x>0),

using the method of undetermined coefficients.