The amount of time it takes on an exam is normally distributed with a mean of 72 minutes and standard deviation 4 minutes. Suppose you take a random sample of 64 students from this population. There would be a 99.7% chance that the sample mean amount of time taken on the exam would be between:

A. 68 and 76 minutes
B. 71 and 73 minutes
C. 70.5 and 73.5 minutes
D. 60 and 84 minutes

Option C) 70.5 and 73.5 minutes

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 72 minutes

Standard Deviation, σ = 4 minutes

Sample size, n = 64

We are given that the distribution of amount of time is a bell shaped distribution that is a normal distribution.

Empirical Formula:

Standard error due to sampling =

Thus, by empirical formula 99.7% of data will lie between:

There would be a 99.7% chance that the sample mean amount of time taken on the exam would be between 70.5 and 73.5 minutes.

Thus, the correct answer is

Option C) 70.5 and 73.5 minutes

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.