Assume we need to estimate the mean of a normally-distributed population with great accuracy. Specifically, for significance level α = .01, we must place a confidence interval around μ such that the width of the interval is no larger than .1. Assume that the variance of the population is known to be σ2. How large must the sample size be to assure that the width of the confidence interval is no larger than .1?

Step-by-step explanation:

We are given the following in the question:

Significance level = 0.01

Width of interval = 0.1

Population variance =

We have to find the sample size so that the width of the confidence interval is no larger than 0.1

Formula for sample size:

where E is the margin of error. Since the confidence interval width is 0.1,

Putting these values in the equation:

So, the above expression helps us to calculate the sample size so that the width of the confidence interval is no larger than 0.1 for different sample variances.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc