Question

A minority representation group accuses a major bank of racial discrimination in its recent hires for financial analysts. Exactly 16% of all applications were from minority members, and exactly 15% of the 2100 open positions were filled by members of the minority.
Required:
a. Find the mean of p, where p is the proportion of minority member applications in a random sample of 2100 that is drawn from all applications.
b. Find the standard deviation of p.

Answer 1

Answer:

a) The mean is of $\mu = 0.16$

b) The standard deviation is of $s = 0.008$

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Question a:

Exactly 16% of all applications were from minority members

This means $p = 0.16$, and thus, the mean is of $\mu = p = 0.16$

b. Find the standard deviation of p.

2100 open positions, thus $n = 2100$.

$s = \sqrt{\frac{p(1-p)}{n}}$

$s = \sqrt{\frac{0.16*0.84}{2100}}$

$s = 0.008$

The standard deviation is of $s = 0.008$