Find the following probabilities for a standard normal random variable z : P(-2<= z <= 2)

dejanimaab

dejanimaab

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2022-08-20

Find the following probabilities for a standard normal random variable z : P(-2<= z <= 2)

Answer & Explanation

ekhonawy

ekhonawy

Beginner2022-08-21Added 6 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(0z2) is given in the row with z=2.0 and in the column with .00 of the normal probability table in the appendix:
P(0z2)=0.4772
The standard normal distribution is symmetric about 0:
P(2z2)=2P(0z2)=2(0.4772)=0.9544

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