Answers, Ch. 6
6.7
m = 9.152, σ =
3.00
a. P ( X > 10.00) = P [ (X - m)
/ σ > (10.00 - 9.152) / 3.00]
= P (Z > 0.28) = 1 - P (Z < 0.28) = 1 - 0.6103 = 0.3897
b. P (3.00 < X < 5.00) = P [(3.00 - 9.152) / 3.00 < (X
- m) / σ < (5.00 -
9.152) / 3.00]
= P (-2.05 < Z < -1.38) = P (Z < -1.38) -
P (Z < -2.05)
= 0.0838 - 0.0202 = 0.0636
c. P (X < 5.00) = P [(X - m) /
σ < (5.00 - 9.152) / 3.00]
= P (Z < -1.38) = 0.0838
d. P (X < X0) = 0.99 => P (Z < Z0)
= 0.99 => Z0 = 2.33
X0 = m + Z0
σ = 9.152 + (2.33)(3.00) =
16.14
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