I want to ask about standard normal distribution. What is the highest and lowest value of z sc

doturitip9

doturitip9

Answered question

2022-07-10

I want to ask about standard normal distribution. What is the highest and lowest value of z score can be?
From the table of standard normal, the value z score is only for -3.99 z 3.99.
Can it be higher than the range? Is there any programme or formula to compute the probability of standard normal distribution for the range outside -3.99 z 3.99?

Answer & Explanation

owerswogsnz

owerswogsnz

Beginner2022-07-11Added 12 answers

The table below shows the values given by R for Φ ( x ) = Pr ( X x ) for some x. In addition Φ ( x ) = Φ ( x ).

For x large and negative, a reasonable approximation is x x 2 + 1 exp ( x 2 / 2 ) 2 π . For example, with x = 15, this gives 3.670825e-51

So for x large and positive, a reasonable approximation is 1 x x 2 + 1 exp ( x 2 / 2 ) 2 π .

x Phi(x) = Pr(X<=x)
-15 3.670966e-51
-14 7.793537e-45
-13 6.117164e-39
-12 1.776482e-33
-11 1.910660e-28
-10 7.619853e-24
-9 1.128588e-19
-8 6.220961e-16
-7 1.279813e-12
-6 9.865876e-10
-5 2.866516e-07
-4 3.167124e-05
-3 1.349898e-03
-2 2.275013e-02
-1 1.586553e-01
0 5.000000e-01
1 8.413447e-01
2 9.772499e-01
3 9.986501e-01
4 9.999683e-01
5 9.999997e-01
ban1ka1u

ban1ka1u

Beginner2022-07-12Added 5 answers

z score that is above 3.999 or below 3.999 is considered highly unusual in Triola book which means that it very rarely occurs. Any other value of z that is greater than 3.999 is treated the same as 3.999 or 3.999 in the case of negative z because P ( | z | > 3.999 ) 0

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