Dr. Jamison gives students 90 minutes to complete the final exam for her course. Most students use almost all the time allowed, and relatively few students finish early, so the distribution of times that it takes students to finish the exam is strongly skewed to the left. The mean and standard deviation of the finishing times are 85 and10minutes, respectively.
Suppose we took random samples of 40 students and calculated x as the sample mean finishing time. We can assume that the students in each sample are independent.
What would be the shape of the sampling distribution of x? Please select one option and then briefly explain:

a) Skewed to the left
b) Skewed to the right
c) Approximately normal
d) Unknown; we don't have enough information to determine the shape.

C

Step-by-step explanation:

Brief explanation

The Sample space represented by 40 students are considered a larger sample size. Consequently, even with the decreasing number of population remaining doing the exam, the distribution of x is approximately normal

(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

5

step-by-step explanation: