# S1 The Normal DistributionWatch

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Thread starter 14 years ago
#1
1) The random variable Z~N (0,1^2). Find:

a) P (Z < 1.455)
b) p (Z > 0.714)

2) The random variable X has a normal distribution with mean 16 and variance 0.64. Find x, such that P (X < x) = 0.025

1a) 0.9279
1b) 0.2389

2) 14.432

Cheers
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14 years ago
#2
(1)
(a) Phi(1.455) = 0.927
(b) 1 - Phi(0.714) = 0.238

(2)
Phi(1.960) = 0.975
x = 16 - 1.960*sqrt(0.64) = 14.432

[Phi = "Standard normal cumulative distribution function".]
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