![4.18 A random sample of size 25 is selected from a population with mean μ = 85 and standard deviation σ-4. Approximate the following probabilities using the central limit theorem (a) PrX 86, 6451 (b) PrX < 84.340] (c) Pr(83.04 〈 X < 86.96]](http://img.homeworklib.com/questions/39279c70-7654-11eb-8e0b-a3cdc2a155b1.png?x-oss-process=image/resize,w_560)
Homework Answers
P(
< A) = P(Z < (A - 
)/
)
Here, 
= 85
=
4
n = 25
By central limit theorem,
= = 85
= 
= 
= 0.8
(a) P(
> 86.645) = 1 - P(
< 86.645)
= 1 - P(Z < (86.645 - 85)/0.8)
= 1 - P(Z < 2.06)
= 1 - 0.9803
= 0.0197
(b) P(
< 84.340) = P(Z < (84.340 - 85)/0.8)
= P(Z < -0.825)
= 0.2047
(c) P(83.04 <
< 86.96) = P(Z < 86.96) - P(Z < 83.04)
= P(Z < (86.96 - 85)/0.8) - P(Z < (83.04 - 85)/0.8)
= P(Z < 2.45) - P(Z < -2.45)
= 0.9929 - 0.0071
= 0.9858
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