on a standard Iq test the scores are normally distributed with a mean of 100 and a standard devaition of 20.

A. if you score 140 in whst precentile are you?
B. if you score 90 on what percentil are you?

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I don't understand how to do it, there are no examples in my book

To calculate the percentile for a specific IQ score on a standard IQ test with a mean of 100 and a standard deviation of 20, you can use the standard normal distribution (also known as the Z-distribution) and the concept of z-scores. Follow the steps below to find the percentiles for the given IQ scores:

A. If you score 140, in what percentile are you?
1. Calculate the z-score:
- Subtract the mean (100) from the given score (140): 140 - 100 = 40.
- Divide the result by the standard deviation (20): 40 / 20 = 2.
- The z-score for a score of 140 is 2.

2. Find the percentile using the z-score:
- Look up the nearest z-score (2) in the standard normal distribution table.
- The table will give you the area under the curve to the left of the z-score.
- In this case, the table will show that the area to the left of z = 2 is approximately 0.9772 or 97.72%.

3. Calculate the percentile:
- Since the IQ scores are normally distributed, the area to the left of the z-score represents the percentile.
- Multiply the area under the curve by 100 to get the percentile: 0.9772 * 100 = 97.72%.
- So, if you score 140, you are approximately in the 97.72th percentile.

B. If you score 90, in what percentile are you?
1. Calculate the z-score:
- Subtract the mean (100) from the given score (90): 90 - 100 = -10.
- Divide the result by the standard deviation (20): -10 / 20 = -0.5.
- The z-score for a score of 90 is -0.5.

2. Find the percentile using the z-score:
- Look up the nearest z-score (-0.5) in the standard normal distribution table.
- The table will give you the area under the curve to the left of the z-score.
- In this case, the table will show that the area to the left of z = -0.5 is approximately 0.3085 or 30.85%.

3. Calculate the percentile:
- Since the IQ scores are normally distributed, the area to the left of the z-score represents the percentile.
- Multiply the area under the curve by 100 to get the percentile: 0.3085 * 100 = 30.85%.
- So, if you score 90, you are approximately in the 30.85th percentile.