1. Given a normal distribution with μ = 40 and σ = 6, find
(a) the area below 32;
(b) the area above 27;
(c) the area between 42 and 51;
(d) the x value that has 45% of the area below it;
(e) the x value that has 13% of the area above it.
Area under a normal curve is equivalent to Probabilities.
μ = 40 and σ = 6
(a) Area below 32
Area below 32 is P(<32)
(b) Area above 27 is P(>27)
(c) Area between 42 and 51 is P(42<x<51)
(d) The x value that has 45% of the area below it
The z-score corresponding to 0.45 on the left tail is -0.12566 (From z tables or =NORM.S.INV(0.45) excel function). Thus,
Solving for x,
(e) The x value that has 13% of the area above it
The z-score corresponding to 0.87 on the left tail is 1.126391 (From z tables or =NORM.S.INV(0.87) excel function). Thus,
Solving for x,
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