SOLUTION: The scores on a statistics test were normally distributed with a mean of 78 and a standard deviation of 7.6. A student who took the test was randomly selected. What is the probabil

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Question 885300: The scores on a statistics test were normally distributed with a mean of 78 and a standard deviation of 7.6. A student who took the test was randomly selected. What is the probability that the student scored higher than 85?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean = 78
standard deviation = 7.6
with a score of 85, the z score would be:
(85 - 78) / 7.6 = .92
from the z-score table, a z score of .92 will have .8212 of the area under the distribution curve to the left of it.
this means that a z score of .92 will have 100 - .8212 = .1788 of the area under the distribution curve to the right it it.
this means that the probability that the student scored higher than 85 is .1788.
the z-score table i used is shown below:
http://lilt.ilstu.edu/dasacke/eco148/ztable.htm
the z score was rounded to 2 decimal places to conform to the capabilities of the z score table.