Question 1168799: Consider a normal distribution curve where 70-th percentile is at 15 and the 15-th percentile is at 1. Use this information to find the mean, 𝜇 , and the standard deviation, 𝜎 , of the distribution.( i don't know where or how to start this i am soooooooooooo lost
a) 𝜇=
b) 𝜎=
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! You want to get two equations in 2 unknowns, like simultaneous equations.
z=(x-mean)/sd. There are four variables, and the x and z are both known, once the percentiles are used to calculate z.
can use invnorm function on calculator 2nd VARS 3 invnorm(0.15,0,1) ENTER
to get z=-1.036 for the 15th percentile (the table could be used, too)
the 70th percentile is z=+0.524
z=(x-mean)/sd
using the first above -1.03=(1-mean)/sd; from the second, 0.5244=(15-mean)/sd
-1.036 sd=1-mean
mean-1.036 sd=1
and
0.524 sd=15-mean
mean+0.544 sd=15
subtract second from first
-1.56 sd=-14
sd=8.97
use first -1.03(8.97)=1-mean
mean=10.29
so mean is 10.29
sd is 8.97
can check in the second equation or use the calculator 2ndVARS 2 normalcdf(1,15,10.30,8.97) looking for an answer of 0.55, since the area in between the 15th and 70th percentiles is 55%. I get 54.99%, which is reasonable given rounding.
If one uses two decimal place z values, which is common, the sd will be a little different.
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