5.2. The Density Curve of the Normal Distribution http://www.ck12.org
Review Answers
- Here is the distribution with a density curve drawn and the inflection points estimated.
The distribution appears to be normal. The inflection points appear to be a little more than two units from
the mean of 84, therefore we would estimate the standard deviation to be a little more than two. Using the
frequencies, the middle three bins contain 42 of the 50 values. Approximately 34 of the values should be
within one standard deviation, which is consistent with our estimate.- 1− 0. 2148 = 0. 7852
2.P(z≤− 1 ) = 0. 1587 ,P(z≤ 1 ) = 0. 8413 , 0. 8413 − 0. 1587 = 0. 6826
3.P(z≤− 1. 56 ) = 0. 0594 ,P(z≤ 0. 32 ) = 0. 6255 , 0. 6255 − 0. 0594 = 0. 5661 - Brielle did not enter the mean and standard deviation. The calculator defaults to the standard nor-
mal curve, so the calculation she performed is actually explaining the percentage of data between the
z−scores of 80 and 90. There is virtually 0 probability of experiencing data that is over 80 standard
deviations away from the mean, especially given a test grade presumably out of 100. - 0.525 or about 53%
- The 78 is a better grade. The percentile for that score is slightly higher, at about 82%, than the 77, which is
only about the 76thpercentile.
1.A90 is a better score with teacherA.