Solution :
Given that ,
1.
mean = = 100
standard deviation = = 20
P(x 90) = 1 - P(x 90)
= 1 - P[(x - ) / (90 - 100) / 20]
= 1 - P(z -0.5)
= 1 - 0.3085
= 0.6915
P(x 90) = 0.6915
2.
a.
mean = = 4.6
standard deviation = = 1.4
P(x < 3.0) = P[(x - ) / < (3.0 - 4.6) / 1.4]
= P(z < -1.14)
= 0.1271
Probability = 0.1271
b.
P(x > 7.0) = 1 - P(x < 7.0)
= 1 - P[(x - ) / < (7.0 - 4.6) / 1.4]
= 1 - P(z < 1.71)
= 1 - 0.9564
= 0.0436
Probability = 0.0436
P(3.0 < x < 7.0) = P[(3.0 - 4.6)/ 1.4) < (x - ) / < (7.0 - 4.6) / 1.4) ]
= P(-1.14 < z < 1.71)
= P(z < 1.71) - P(z < -1.14)
= 0.9564 - 0.1271
= 0.8293
Probability = 0.8293
Assume that x has a normal distribution with the specified mean and standard deviation. Find the...
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