Question

x is normally distrubited with mean 10 and standard deviation of 2. find the following probility . a. p(-2<x<8) b. find x such that p(x<x<10)=0.2

Answer 1

a)

Given :- = 10 , = 2 )
We convet this to Standard Normal as
P(X < x) = P( Z < ( X - ) / )
P ( -2 < X < 8 ) = P ( Z < ( 8 - 10 ) / 2 ) - P ( Z < ( -2 - 10 ) / 2 )
= P ( Z < -1) - P ( Z < -6 )
= 0.1587 - 0
= 0.1587

b)

P(x < X < 10) = 0.2

P(X < 10) - P(X < x) = 0.2

P(Z < (10 - 10) / 2) - P(Z < x) = 0.2

P(Z < 0) - P(X < x) = 0.2

0.5 - P(X < x) = 0.2

P(X < x) = 0.3

P(Z < ( x - ) / ) = 0.3

From Z table, z-score for the probability of 0.3 is -0.5244

( x - 10) / 2 = -0.5244

x = 8.95