Math, asked by rohansehrawat6014, 11 months ago

If X  N (50, 16) then which of the following is not possible: (a) P (X > 60) = 0.30 (b) P (X < 50) = 0.50 (c) P (X < 60) = 0.40 (d) P (X > 50) = 0.50

Answers

Answered by amitnrw
4

Given :  X ~ N (50, 16)  

To find : which of the following is not possible.

(a) P (X > 60) = 0.30 (b) P (X < 50) = 0.50 (c) P (X < 60) = 0.40 (d) P (X > 50) = 0.50

Solution:

X ~ N (50, 16)  

=> Mean =  50

    SD = 16

Z score =  (Value - Mean)/SD

P (X > 60) = 0.30

for X  > 60

=> Z Score = (60 - 50)/16 = 10/16  =  0.625    

Z Score for  0.625      = 0.734

for X  > 60 => 1  -0.734  =   0.266        

P (X > 60) = 0.266

Hence P (X > 60) = 0.30 is not possible

P (X < 60) = 0.734

P (X < 60) = 0.40   not possible

P (X < 50) = 0.50    

=> Z Score = (50 - 50)/16 =  0  

Z score 0 = 0.5    & 1 - 0.5 = 0.5

P (X < 50) = 0.50     is possible

P (X > 50) = 0.50  is possible

if we do not use exact z score values

then for X  < 60

60 is more than 50

hence P(X < 60) would be more than 0.5

hence can not be = 0.4

hence  P(X < 60)  = 0.4 not possible

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