Question 728181: I have an extra credit sheet, 25 problems similar to these two. Can someone help with an explanation to solve both? Appreciation is unlimited.
Use the empirical, otherwise known as the 68 - 95 - 99.7 rule.
1) Distribution is normal. Mean is 10, Standard Deviation is 2, find the percentage of values in the distribution: BELOW 10
AND
2) Mean is 12, Standard Deviation is 3, find percentage of values in the distribution: ABOVE 18.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
68 percent is within 1 standard deviation of the mean, and 95 percent is within 2 standard deviations of the mean. Normal distribution means that half of the data is above the mean and half below.
So for problem 2, if the mean is 12 and the sd is 3, then 18 is exactly 2 standard deviations above the mean. We know that 95 percent of the data is within 2 standard deviations of the mean, so half of 95 percent, namely 47.5% is within 2 sd below the mean and the other 47.5% is within 2 sd above the mean. So, adding it all up, 50% is below the mean, then 47.5 is 2 sd above the mean. Hence 97.5% of the data is less than or equal to 18. Therefore 1 - 0.975 = 0.025 or 2.5% is greater than or equal to 18.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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