Scores on a statistics final in a large class were normally distributed with a mean of 75 and standard deviation of 6. What is the 40th percentile of the scores?

1 Answer
Sep 23, 2016

#40^(th)# percentile is #73.48#.

Explanation:

#40^(th)# percentile means a point on the normal curve, at which area of the curve to its left is #40%# of total area under the curve. Now from tables it is equivalent to a #z#-score of #-0.2533#.

As the relation between a #z#-score and its actual value for normal distribution is given by #z=(x-mu)/sigma# or #x=zxxsigma+mu#, where #mu# is mean and #sigma# is standard deviation,

The #40^(th)# percentile is given by #-0.2533xx6+75#

= #-1.5198+75=73.4802#

Hence #40^(th)# percentile is #73.48#.
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