A particular group of men have heights with a mean of 181 cm and a standard deviation of 6 cm. Earl had a height of 196 cm. a. What is the positive difference between Earl's height and the mean? b. How many standard deviations is that [the difference found in part (a)]? c. Convert Earl's height to a z score. d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Earl's height usual or unusual?

a. 15

b. based on the result of part a, 15 standard deviation above the mean.

c. 2.5

d.  Earl's height is unusual

Step-by-step explanation:

We have that "x" would be the height of Earl = 196, the mean m = equals 181 and the standard deviation (sd) = 6, now:

a. the positive difference between the mean and Earl's height:

D = x - m

D = 196 - 181 = 15

b. based on the result of part a, 15 standard deviation above the mean.

c. The z value is given by:

z = x - m / sd

replacing:

z = (196 - 181) / 6

z = 2.5

d. the z-score is unusual since the value of z is 2.5 which is a value greater than than 2 standard deviations above the mean, which means that Earl's height is unusual

17.08

correct me if i am wrong.

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