Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(−e<z<e)=0.2128, what is e?

Luciano Webster

Luciano Webster

Answered question

2022-07-16

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P ( - e < z < e ) = 0.2128 , what is e?

Answer & Explanation

Reinfarktq6

Reinfarktq6

Beginner2022-07-17Added 18 answers

e = 0.27
Explanation:we have
Z ~ N ( 0 , 1 )
The Normal Distribution tables give probabilities for
P ( z < x ) so we need to adjust what we need to what the tables give us
P ( - e < z < e ) = 2 P ( 0 < z < e )
by the symmetrical property of the Normal.
P ( 0 < z < e ) = 0.1064
now to use the tables we have to add
P ( - < z < 0 ) = 0.5
P ( z < e ) = 0.6064
Using the tables in reverse we find
e = 0.27

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