ACT mathematics score for a particular year are normally distributed with a mean of 28 and a standard deviation of 2.4 points

A. What is the probability a randomly selected score is greater than 30.4?

B. what is the probability a randomly selected score is less than 32.8?

C. What is the probability a randomly selected score is Between 25.6 and 32.8?

A) 0.1587

B) 0.9772

C) 0.8185

Step-by-step explanation:

A)

In this problem, the mathematics score of the year is distributed according to a normal distribution, with parameters:

is the mean of the distribution

is the standard deviation of the distribution

We want to find the probability that a randomly selected score is greater than 30.4. First of all, we calculated the z-score associated to this value, which is given by:

The z-score tables give the probability that the z-score is less than a certain value; since the distribution is symmetrical around 0,

Here we want to find , which is therefore equivalent to . Looking at the z-tables, we find that

B)

Here instead we want to find the probability that a randomly selected score is less than 32.8.

First of all, we calculate again the z-score associated to this value:

Now we notice that:

(1)

Since the overall probability under the curve must be 1. We also note that (from part A)

Which means that we can rewrite (1) as

Here, we have

Z = 2

This means that

Looking at the z-tables, we find that

Therefore, we get

C)

Here we want to find the probablity that the score is between 25.6 and 32.8.

First of all, we calculate the z-scores associated to these two values:

So here we basically want to find the probability that

Which can be rewritten as:

So in this case,

From part A and B we found that:

Therefore,

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

answer: the correct answer is -32

step-by-step explanation: