Solution :
a )Given that,
mean =
= 5
standard deviation =
= 4
P (0 < x < 6 )
P ( 0 - 5 / 4) < ( x - /
) < ( 6 - 5 /4)
P ( -5 / 4 < z < 1 / 4 )
P (-1.25 < z < 0.25)
P ( z < 0.25 ) - P ( z < -1.25)
Using z table
= 0.5987 - 0.1056
= 0.4931
Probability = 0.4931
b )Given that,
mean =
= 5
standard deviation =
= 5
P (0 < x < 6 )
P ( 0 - 5 / 5) < ( x - /
) < ( 6 - 5 / 5)
P ( - 5 / 5 < z < 1 / 5 )
P (-1 < z < 0.2)
P ( z < 0.2 ) - P ( z < -1)
Using z table
= 0.5793 - 0.1587
= 0.4206
Probability = 0.4206
c ) Given that,
mean =
= 4
standard deviation =
= 4
P (0 < x < 6 )
P ( 0 - 4 / 4) < ( x - /
) < ( 6 - 4 / 4)
P ( - 4 / 4 < z < 2 / 4 )
P (-1 < z < 0.5)
P ( z < 0.5 ) - P ( z < -1)
= 0.6915 - 0.1587
= 0.5328
Probability = 0.5328
d ) Given that,
mean =
= 6
standard deviation =
= 2
P (x > 1 )
= 1 - P (x < 1 )
= 1 - P ( x - /
) < ( 1 -6 / 2)
= 1 - P ( z <- 5 / 2 )
= 1 - P ( z < -2.5)
Using z table
= 1 - 0.0062
= 0.9938
Probability = 0.9938
e ) Given that,
mean =
= 0
standard deviation =
= 2
P (x > 1 )
= 1 - P (x < 1 )
= 1 - P ( x - /
) < ( 1 - 0 / 2)
= 1 - P ( z < 1 / 2 )
= 1 - P ( z < 0.50)
Using z table
= 1 - 0.6915
= 0.3085
Probability = 0.3085
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