How do I turn a z value into an x value? The example in class was this: IQ scores are normally distributed with a mean of 100 and a standard deviation of 16. Find the 95th percentile. The answer was 126.32. I attached a picture of the example. I would really appreciate it if you could write an explanation for each step. ,9495 Teacher took3. Identifying Extreme Values: Using the Normal Table in ReverseSteps:1) Sketch the normal curve associated with the variable and locate the point that is of interest.2) Use the standard normal table to obtain the z value corresponding to the point found in Step 1.3) Obtain the x value having the z value found in Step 2. The following formula can be used toM=D1005%60=D16find the x value: x=z.o+H.Example 6.4: Consider the IQ Scores in Example 6.2.a. Find the 95th percentile of IQ scores..1009505Teacher toolkthe averageX-10016li645= X-100To%3DX= 1.645 x16 + l00 = 126.3%3Db. Find the IQ score separating the bottom 10% from the top 90%.534 1003-1.28=x-10016-1,28x16+100%3D79.52Example 6.5: A mandatory competency test for high school sophomores has a normal distributionwith a mean of 400 and a standard deviation of 100.I den + c ot

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Answered: 3. Identifying Extreme Values: Using…

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Author:Amos Gilat

Publisher:Amos Gilat

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How do I turn a z value into an x value?

The example in class was this: IQ scores are normally distributed with a mean of 100 and a standard deviation of 16. Find the 95th percentile. The answer was 126.32.

I attached a picture of the example.

I would really appreciate it if you could write an explanation for each step.

,9495 Teacher took
3. Identifying Extreme Values: Using the Normal Table in Reverse
Steps:
1) Sketch the normal curve associated with the variable and locate the point that is of interest.
2) Use the standard normal table to obtain the z value corresponding to the point found in Step 1.
3) Obtain the x value having the z value found in Step 2. The following formula can be used to
M=D100
5%60=D16
find the x value: x=z.o+H.
Example 6.4: Consider the IQ Scores in Example 6.2.
a. Find the 95th percentile of IQ scores.
.100
9505
Teacher toolk
the average
X-100
16
li645= X-100
To
%3D
X= 1.645 x16 + l00 = 126.3
%3D
b. Find the IQ score separating the bottom 10% from the top 90%.
534 1003
-1.28=x-100
16
-1,28
x16+100%3D79.52
Example 6.5: A mandatory competency test for high school sophomores has a normal distribution
with a mean of 400 and a standard deviation of 100.
I den + c ot

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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