Question

5. Find the 35th and the 85th percentiles. Provide the meaning of these statistics

Answer 1

Solutiom :-

The ' z ' Distribution of the 35 th % is,

P ( Z < z ) = 35 %

By Using Standard Normal table,

P ( Z < - 0.385 ) = 0.35

z = - 0.385

Therefore, it is concluded that the corresponding z-score associated to the given 35-th percentile is z = -0.385

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The ' z ' Distribution of the 35 th % is,

P ( Z < z ) = 85 %

By Using Standard Normal table,

P ( Z < 1.036 ) = 0.85

z = 1.036

Therefore, it is concluded that the corresponding z-score associated to the given 85-th percentile is z = 1.036

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For a given percentile p, which is a number between 0-1, finding the corresponding z-score is done by finding the value of z that solves the following:

Pr ( Z < z ) = P

The 35th percentile means that 35 percent or more is above you and 65 percent is below you. The percentile is a way of illustrating how common your result is compared to others.

The 85th percentile means that 85 percent or more is above you and 15 percent is below you. The percentile is a way of illustrating how common your result is compared to others.