Answer:
ha
Step-by-step explanation:
Using the <em>normal distribution and the central limit theorem</em>, it is found that there is a 0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:

- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem:
- The mean is of 660, hence
.
- The standard deviation is of 90, hence
.
- A sample of 100 is taken, hence
.
The probability that 100 randomly selected students will have a mean SAT II Math score greater than 670 is <u>1 subtracted by the p-value of Z when X = 670</u>, hence:

By the Central Limit Theorem



has a p-value of 0.8665.
1 - 0.8665 = 0.1335.
0.1335 = 13.35% probability that 100 randomly selected students will have a mean SAT II Math score greater than 670.
To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213
Alright, let's convert to decimals for these calculations: fractions could get messy.
1/5 = .2
1/2 = .5
Imagine a rectangular solid in your mind. How many sides does it have?
6. In the image shown you have 3 facing you. In addition to those, there are 3 not shown. They will correspond to the calculations you make on the front, though, so all you have to do is double the values you get.
Area is length * width, or length * height, or width * height. So:
A = 3.2 (length) * 4.5 (height) for the front face of the rectangular solid(as well as the back face.)
A = 5 (width) * 4.5 (height) for the right face of the rectangular solid (and the one on the left, away from you.)
A = 3.2 (length) * 5 (width) for the top of the solid(and the bottom).
Calculating these values, we get that
A=14.4
A=22.5
A= 16
So that's 3 out of 6 values for the full surface area.
Like I said though, these values can merely be doubled for the complete area.
Add these three together:
14.4+22.5+16=52.9
multiply by 2 to account for the other 3 sides
52.9 * 2 = 105.8
105.8 is the surface area.
7/10 is 7 pieces of the whole. The whole would be cut into 10 pieces and you have 7 of the 10...7/10.