Answer:
Given,
Mean = 79
standard deviation = 8
a)
To give proportion of scores were above 93
P(x > 93)
= P((x - mu)/s > (93 - 79)/8)
= P(z > 1.75)
= 0.0400592 [since from z table]
= 0.0401
b)
P(X < 66)
= P((x - mu)/s < (66 - 79)/8)
= P(z < -1.625)
= 0.0520813 [since from z table]
= 0.0521
c)
P(70 < x < 90)
= P((70 - 79)/8 < (x-mu)/s < (90 - 79)/8)
= P(-1.125 < z < 1.375)
= P(z < 1.375) - P(z < -1.125)
= 0.9154342 - 0.1302945 [since from z table]
= 0.7851
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