1. ## Standard Deviation Questions

67. On a standard IQ test, the scores are normally distributed with a mean of 100 and a standard deviation of 20.

a) If you score 140, in what percentile are you?

b) If you score 90, in what percentile are you?

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68. Eldon received 72 on his first calculus test. The marks were normally distributed with a mean of 60 and a standard deviation of 8. He received 80 on the next test, which was normally distributed with a mean of 75 and a standard deviation of 6. Which was the better mark, relatively speaking?

2. Originally Posted by cnmath16
67. On a standard IQ test, the scores are normally distributed with a mean of 100 and a standard deviation of 20.

a) If you score 140, in what percentile are you?

b) If you score 90, in what percentile are you?

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68. Eldon received 72 on his first calculus test. The marks were normally distributed with a mean of 60 and a standard deviation of 8. He received 80 on the next test, which was normally distributed with a mean of 75 and a standard deviation of 6. Which was the better mark, relatively speaking?
Q20 (a) You need to first calculate Pr(X < 140) = Pr(Z < 2).

Note: $Z = \frac{X - \mu}{\sigma} = \frac{140 - 100}{20} = 2$.

Now apply the definition of percentile.

Q20 (b) You need to first calculate Pr(X < 90) = Pr(Z < -1/2).

Now apply the definition of percentile.

Note: $Z = \frac{X - \mu}{\sigma} = \frac{90 - 100}{20} = -\frac{1}{2}$.

Q68 Calculate the z-score for each test mark: $Z = \frac{X - \mu}{\sigma}$.

The larger z-score corresponds to the better test mark.

3. Ok, thanks for your help. Here are my answers. Please tell me if they are correct or not.

67.
a) If you score 140..
Mean (x) = 100, Standard deviation (s) = 20
140 is 50 marks above x
140 is 40/20 or 20 above x

Area below 20 above x = 0.4772+ 0.5
= 0.9772

Therefore, You would be in the 98th percentile.

b) If you score 90..
x = 100 s= 20
90 is 10 marks below x
90 is 10/200 or 1/20 below x
Area below 1/20 (s) below x = 0.5-0.1915
= 0.3085

Therefore, you would be in the 31st percentile

4. Originally Posted by cnmath16
Ok, thanks for your help. Here are my answers. Please tell me if they are correct or not.

67.
a) If you score 140..
Mean (x) = 100, Standard deviation (s) = 20
140 is 50 marks above x
140 is 40/20 or 20 above x

Area below 20 above x = 0.4772+ 0.5
= 0.9772

Therefore, You would be in the 98th percentile.

b) If you score 90..
x = 100 s= 20
90 is 10 marks below x
90 is 10/200 or 1/20 below x
Area below 1/20 (s) below x = 0.5-0.1915
= 0.3085

Therefore, you would be in the 31st percentile
If you're to give an answer correct to the nearest whole percentile, then your answers are correct.