The lengths of text messages are normally distributed with a population standard deviation of 6 characters and an unknown population mean. If a random sample of 27 text messages is taken and results in a sample mean of 25 characters, find a 95% confidence interval for the population mean. Round your answers to two decimal places. z0.10 z0.05 z0.04 z0.025 z0.01 z0.005 1.282 1.645 1.751 1.960 2.326 2.576 You may use a calculator or the common z-values above.

(22.74 ; 27.26)

Step-by-step explanation:

The confidence interval relation is stated as :

Mean ± Zcritical * σ/sqrt(n)

Mean = 25

σ = 6

The Zcritical at 95% = 1.96

Hence,

25 ± 1.96 * (6/sqrt(27))

25 ± 1.96 * 1.1547005

Lower boundary :

25 - (1.96 * 1.1547005) = 22.73678702

Upper boundary :

25 + (1.96 * 1.1547005) = 27.26321298

(22.74 ; 27.26)

5050 i think

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