Answer:
And for this case we can use the complement rule and the normal standard distribution of excel and we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
And we select a sample size of n =70
From the central limit theorem (n>30)we know that the distribution for the sample mean is given by:
And we want to find this probability:
And we can use the z score formula given by:
And using this formula we got:
And for this case we can use the complement rule and the normal standard distribution of excel and we got:
So this table is all about showing you how to calculate the standard deviation in various steps.
Step 1: calculate the average (=mean) of the x values. You probably know how to do this, add all values and divide by the number of values. (53+51+48+49+37)/5 = 47.6. This is your .
Step 2: calculate . This is the "distance" of your x value to the average. This has been done for you already in the second column. E.g. 53-47.6=5.4.
Step 3: square the results of . This is also done for you already, it is the third column.
Step 4: Add (sum) the values. So add the third column. I get 155.2 when I do that.
Step 5: Divide that sum by the number of x values. 155.2/5 = 31.04 ≈ 31. That number is your variance right there!
Step 6: Take the square root of the variance. √31.04 ≈ 5.571 ≈ 5.6. This is your standard deviation.
Each number contains a different amount than others.
<span>Simplifying
5x + 3 = 10x + -17
Reorder the terms:
3 + 5x = 10x + -17
Reorder the terms:
3 + 5x = -17 + 10x
Solving
3 + 5x = -17 + 10x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-10x' to each side of the equation.
3 + 5x + -10x = -17 + 10x + -10x
Combine like terms: 5x + -10x = -5x
3 + -5x = -17 + 10x + -10x
Combine like terms: 10x + -10x = 0
3 + -5x = -17 + 0
3 + -5x = -17
Add '-3' to each side of the equation.
3 + -3 + -5x = -17 + -3
Combine like terms: 3 + -3 = 0
0 + -5x = -17 + -3
-5x = -17 + -3
Combine like terms: -17 + -3 = -20
-5x = -20
Divide each side by '-5'.
x = 4
Simplifying
x = 4</span>
Check if it's odd, and then divide by every odd number between one and itself.