Asurvey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.
construct the 95 % confidence interval for the true proportion of all voters in the state who favor approval.

a) 0.435 < p < 0.508

b) 0.444 < p < 0.500

c) 0.471 < p < 0.472

d) 0.438 < p < 0.505

D) 0.438 < p < 0.505

Step-by-step explanation:

We know that the confidence interval for population proportion is given by :-

, where n= sample size

= Sample proportion.

z* = critical value.

Given : A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.

i.e. n= 865

Two-tailed critical avlue for 95% confidence interval : z* = 1.96

Then, the 95 % confidence interval for the true proportion of all voters in the state who favor approval will be :-

Thus, the required 95% confidence interval : (0.438, 0.505)

Hence, the correct answer is D) 0.438 < p < 0.505

step-by-step explanation:

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