Question 728181
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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
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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