2. stanford–binet iq test scores are normally distributed with a mean score of 100 and a standard deviation of 15. a. sketch the distribution of stanford–binet iq test scores. b. write the equation that gives the z score corresponding to a stanford–binet iq test score. sketch the distribution of such z scores. c. find the probability that a randomly selected person has an iq test score i. over 145. ii. under 91

0.0010,0.2743

Step-by-step explanation:

Given that Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 15

If x represents the scores then

X is N(100,15)

a) See enclosed file

b) Z score =

c) the probability that a randomly selected person has an IQ test score

i. Over 145.

=

ii. Under 91

=

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240