Let X be a continuous random variable distributed by N(5,0.2) find,
A) P(5.9 < X < 5.9)
B) P( 4.6 =< X =< 5.3)
C) P(5.6=< X < 5.7)
D) P( 5.1< X =< 5.7)
Solution :
Given that ,
mean = = 5
standard deviation = = 0.2
A) P( 5.9 < x < 5.9) = P[( 5.9 - 5)/ 0.2) < (x - ) / < (5.9 - 5) / 0.2) ]
= P( 4.5 < z < 4.5)
= P(z < 4.5) - P(z < 4.5)
Using z table
= 1 - 1
= 0
B) P( 4.6 x 5.3 )
= P[(4.6 - 5 / 0.2) (x - ) / ( 5.3 - 5 / 0.2) ]
= P(-2.00 z 1.50 )
= P(z 1.50 ) - P(z -2.00)
Using z table
= 0.9332 - 0.0228
= 0.9104
C) P( 5.6 x < 5.7 )
= P[(5.6 - 5 )/0.2 ) (x - ) / < ( 5.7 - 5) / 0.2) ]
= P(3.00 < z < 3.50)
= P(z < 3.50 ) - P(z < 3.00 )
Using z table
= 0.9999 - 0.9987
= 0.0012
D) P(5.1 < x 5.7 )
= P[(5.1 - 5 )/0.2 ) (x - ) / < ( 5.7 - 5) / 0.2) ]
= P(0.50 < z < 3.50)
= P(z < 3.50 ) - P(z < 0.50 )
Using z table
= 0.9999 - 0.6915
= 0.3084
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