Linear equation 5v=-6v-33
1 answer:
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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
The answer is 1.) 6^1/6
The third root of something is the same as an exponent to the 1/3 power.
(When an exponent is a fraction, the numerator is powers and the denominator finds the root. For example: 3 to the power of 4/2 is multiplied by itself 4 times (81) then the denominator, 2, means we find the square root of it (9). 4/2=2, and 3 to the 2nd power is also 9.)
So that would be 6 to the 1/3 power, then you find the square root of that, so it's (6 to the 1/3 power) to the 1/2 power, and according to the Power Rule (a power on top of a power means you multiply the two powers), that would end up being 1/6.
![\sqrt{ \sqrt[3]{6} } = \sqrt{ {6}^{ \frac{1}{3} } } = (6 { \frac{1}{3} })^{ \frac{1}{2} } = {6}^{ \frac{1}{3} \times \frac{1}{2} } = {6}^{ \frac{1}{6} }](https://tex.z-dn.net/?f=%5Csqrt%7B%20%20%5Csqrt%5B3%5D%7B6%7D%20%20%7D%20%20%3D%20%20%5Csqrt%7B%20%7B6%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%20%7D%20%20%3D%20%286%20%7B%20%5Cfrac%7B1%7D%7B3%7D%20%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%3D%20%20%7B6%7D%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%3D%20%20%7B6%7D%5E%7B%20%5Cfrac%7B1%7D%7B6%7D%20%7D%20)
The third root of something is the same as an exponent to the 1/3 power.
(When an exponent is a fraction, the numerator is powers and the denominator finds the root. For example: 3 to the power of 4/2 is multiplied by itself 4 times (81) then the denominator, 2, means we find the square root of it (9). 4/2=2, and 3 to the 2nd power is also 9.)
So that would be 6 to the 1/3 power, then you find the square root of that, so it's (6 to the 1/3 power) to the 1/2 power, and according to the Power Rule (a power on top of a power means you multiply the two powers), that would end up being 1/6.