Construct a 95% confidence interval for the population mean, µ. assume the population has a normal distribution. a sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2.

Step-by-step explanation:

We want to determine a 95% confidence interval for the mean mean test score of students.

Number of sample, n = 25

Mean, u = 81.5

Standard deviation, s = 10.2

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z score ×standard deviation/√n

It becomes

81.5 ± 1.96 × 10.2/√25

= 81.5 ± 1.96/× 2.04

= 81.5 ± 3.9984

The lower end of the confidence interval is 81.5 - 3.9984 =77.5

The upper end of the confidence interval is 81.5 + 3.9984 = 85.5

Therefore, with 95% confidence interval, the mean test score of students is between 77.5 and 85.5

it is true

step-by-step explanation:

all the combinations add up i used   calculator

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