Find the following probabilities for a standard normal random variable z : P(-1 <= z<= 1)

Nashorn0o

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2022-08-18

Find the following probabilities for a standard normal random variable z : P(-1 <= z<= 1)

Answer & Explanation

Olive Avila

Olive Avila

Beginner2022-08-19Added 7 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) is given in the row with z=1.0 and in the column with .00 of the normal probability table in the appendix:
P(0z1)=0.3413
The standard normal distribution is symmetric about 0:
P(1z1)=2P(0z1)=2(0.3413)=0.6826

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