Respuesta :
Answer:
Positive z-values that are not outliers: (0, 2.68)
Negative z-values that are not outliers: (-2.68, 0)
Step-by-step explanation:
Outliers are data values that are different from all the values in the data set, i.e. they are either too large or too small.
In case of a normal distribution outliers are values that are either more than [Q₃ - (1.5 × IQR)] or less than [Q₁ - (1.5 × IQR)].
Here Q₁ is the first quartile defined as the value that is more than the above 25% of the observation and Q₃ is the third quartile defined as the value that is more than the above 75% of the observations.
In case of a Normal distribution the first quartile (Q₁) is,
P (Z <-0.67) = 0.25
And the third quartile (Q₃) is,
P (Z < 0.67) = 0.75
Then the inter-quartile range (IQR) is:
[tex]IQR=Q_{3}-Q_{1}=0.67-(-0.67)=1.34[/tex]
Then the outliers are:
[tex]Outlier>Q_{3} + (1.5 \times IQR)=0.67+(1.5\times 1.34)=2.68\\Outlier<Q_{3} - (1.5 \times IQR)=-0.67-(1.5\times 1.34)=-2.68\\[/tex]
Then the positive z values that are not considered as outliers are in the range (0, 2.68) and the negative z values that are not considered as outliers are in the range (-2.68, 0).
**The round bracket indicates that the values 0, 2.68 and -2.68 are not included in the respective intervals.
