Question

Which of the following statements about the percentiles for the standard normal distribution are correct? A. The 90th percentile is approximately –1.28 B. The 10th percentile is approximately 1.28 C. The 75th percentile is approximately .67 D. The15th percentile is approximately 1.04 E. None of the above answers is correct

Answer 1

Answer:

Correct option: (C) The 75th percentile is approximately 0.67

Step-by-step explanation:

The pth percentile is a data value such that at least p% of the data set is less than or equal to this data value and at least (100 - p)% of the data set are more than or equal to this data value.

If x is the pth percentile of a data set then,

P (X < x) = p/100

If $X\sim N(\mu, \sigma^{2})$ then  $Z=\frac{X-\mu}{\sigma}$, is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, $Z \sim N (0, 1)$.

• The 90th percentile of a standard normal distribution is:

        P (Z < z) = 0.90, then z = 1.28

• The 10th percentile of a standard normal distribution is:

        P (Z < z) = 0.10, then z = -1.28

• The 75th percentile of a standard normal distribution is:

        P (Z < z) = 0.75, then z = 0.67

• The 15th percentile of a standard normal distribution is:

        P (Z < z) = 0.15, then z = -1.04

Thus, the correct statement is (C).