Answer:
x=3
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:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
- 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:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
By the Central Limit Theorem
![Z = \frac{X - \mu}{s}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7Bs%7D)
![Z = \frac{670 - 660}{9}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B670%20-%20660%7D%7B9%7D)
![Z = 1.11](https://tex.z-dn.net/?f=Z%20%3D%201.11)
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
The value of x is -3.5
Because dividing both sides by -2.4 is going to get you a value of -3.5. And a negative divided by a negative is a positive. :D
Find your common denominator
which is 4y so multiply 4y to both fractions which means top and bottom
your final answer is
36 -y
------
4y
1/2 + 1 1/2 + 1/3. you need to change them so that they all have a common denominator and that would be 3/6 + 1 3/6 + 2/6. that's gives you 1 8/6 which equals 2 2/6 which in simplest form is 2 1/3