Find the following probabilities for a standard normal random variable z : P(-.42<z<1.96)

Johan Patton

Johan Patton

Open question

2022-08-19

Find the following probabilities for a standard normal random variable z :
P(.42<z<1.96)

Answer & Explanation

Payten Daniels

Payten Daniels

Beginner2022-08-20Added 11 answers

Definitions
Complement rule:
P(AC)=P(¬ A)=1P(A)
Addition rule for disjoint or mutually exclusive events:
P(AB)=P(A or B)=P(A)+P(B)
Solution
The probability P(0z1.96) is given in the row with z=1.9 and in the column with .06 of the normal probability table in the appendix:
P(0z1.96)=0.4750
The probability P(0z0.42) is given in the row with z=0.4 and in the column with .02 of the normal probability table in the appendix. The standard normal distribution is symmetric about 0:
P(0.42z0)=P(0z0.42)=0.1628
Add the corresponding probabilities:
P(0.42z1.96)=P(0z1.96)+P(0.42z0)
=0.4750+0.1628=0.6378

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