Solution :
Given that ,
mean =
= 5
standard deviation =
= 1.2
(a)
P(x < 4.5) = P[(x -
) /
< (4.5 - 5) / 1.2]
= P(z < -0.42)
= 0.3372
Probability = 0.3372
(b)
P(x > 5.25) = 1 - P(x < 5.25)
= 1 - P[(x -
) /
< (5.25 - 5) / 1.2)
= 1 - P(z < 0.21)
= 1 - 0.5832
= 0.4168
Probability = 0.4168
(c)
P(4.5 < x < 5.25) = P[(4.5 - 5)/ 1.2) < (x -
) /
<
(5.25 - 5) / 1.2) ]
= P(-0.42 < z < 0.21)
= P(z < 0.21) - P(z < -0.42)
= 0.5832 - 0.3372
= 0.2460
Probability = 0.2460
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