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.

a) The mean is of

b) The standard deviation is of

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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 and standard deviation

Question a:

Exactly 16% of all applications were from minority members

This means , and thus, the mean is of

b. Find the standard deviation of p.

2100 open positions, thus .

The standard deviation is of

c - they will have the same distribution

step-by-step explanation:

this is the only one that could make sense. : )