Suppose that the mean score for the mathematics test cited in Problem 7 is 610. What is the probability that a random sample of 225 students will have a mean score of more than 625

Reference from question 7 :

Standard deviation (σ) = 120

Standard Error = 8

0.0304

Step-by-step explanation:

Sample size (n) = 225

Sample mean = 625

Population mean = 610

Using the relation :

Z = (sample mean - population mean) / σ/√n

Z = (625 - 610) / (120/√225)

Z = 15 / (120/15)

Z = 15 / 8

Z = 1.875

P(mean score of more than 625)

P(Z > 1.875) = 1 - p(Z < 1.875)

p(Z < 1.875) = 0.9696

P(Z > 1.875) = 1 - p(Z < 1.875) = 1 - 0.9696 = 0.0304

(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

yes

step-by-step explanation:

yes