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Answer:
Correct option: (C) The 75th percentile is approximately 0.67
Step-by-step explanation:
The <em>p</em>th percentile is a data value such that at least <em>p</em>% of the data set is less than or equal to this data value and at least (100 - <em>p</em>)% of the data set are more than or equal to this data value.
If <em>x</em> is the <em>p</em>th percentile of a data set then,
P (X < x) = p/100
If then
, is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is,
.
- The 90th percentile of a standard normal distribution is:
P (Z < z) = 0.90, then <em>z</em> = 1.28
- The 10th percentile of a standard normal distribution is:
P (Z < z) = 0.10, then <em>z</em> = -1.28
- The 75th percentile of a standard normal distribution is:
P (Z < z) = 0.75, then <em>z</em> = 0.67
- The 15th percentile of a standard normal distribution is:
P (Z < z) = 0.15, then <em>z</em> = -1.04
Thus, the correct statement is (C).