Question
The random variable X follows normal distribution.P(X<35)=0.2 and P(35<X<45)=0.65.Find mean and standard deviation.
Answer as fast as possible.
Answer as fast as possible.
Answers
PsyDAG
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability and convert it to standard deviations.
For example: P < .2 is approximately -.84 SD.
Continue with your other data.
For example: P < .2 is approximately -.84 SD.
Continue with your other data.
Reiny
Again using
http://davidmlane.com/normal.html
with setting on "value from an area"
if P(X<35)=0.2 and P(35<X<45)=0.65 then P(x<45) = .85
entering .2 and clicking below gave me a z-score of -.841
(35-m)/s = -.841 ---> m - .841s = 35
entering .85 and clicking below gave me a z-score of 1.036
(45-m)/s = 1.036 ----> m + 1.036s = 45
subtract those two equations:
1.877s = 10
s = 5.3277
m = 39.48
http://davidmlane.com/normal.html
with setting on "value from an area"
if P(X<35)=0.2 and P(35<X<45)=0.65 then P(x<45) = .85
entering .2 and clicking below gave me a z-score of -.841
(35-m)/s = -.841 ---> m - .841s = 35
entering .85 and clicking below gave me a z-score of 1.036
(45-m)/s = 1.036 ----> m + 1.036s = 45
subtract those two equations:
1.877s = 10
s = 5.3277
m = 39.48
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