Answer:
[tex]z = -0.340[/tex]
Step-by-step explanation:
We are given that Z is a standard normal variable.
We have to find the value of z such that
P(Z > z) = 0.6331
[tex]P( Z > z)=0.6331[/tex]
[tex]= 1 -P( Z \leq z)=0.6331 [/tex]
[tex]=P( Z \leq z)=1 - 0.6331 = 0.3669 [/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z \leq -0.340) = 0.3669[/tex]
Thus,
[tex]z = -0.340[/tex]
The value of z that satisfies P(Z > z) = 0.6331 is -0.34.
Z score is used to determine by how many standard deviations the raw score is above or below the mean, The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score, \mu=mean,\sigma=standard\ deviation[/tex]
P(Z > z) = 0.6331
P(Z < z) = 1 - P(Z > z) = 1 - 0.6331 = 0.3669
z = -0.34
From the normal distribution table, the value of z that satisfies P(Z > z) = 0.6331 is -0.34.
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