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

14%

of the

2100

open positions were filled by members of the minority.

1. 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.
2. Find the standard deviation of

   p

   .
3. Compute an approximation for

   P≤p0.14

   , which is the probability that there will be

   14%

   or fewer minority member applications in a random sample of

   2100

   drawn from all applications. Round your answer to four decimal places.

Answer 1

Solution:

Given:

p = Population proportion of applications were from minority members = 0.16

Sample size = n = 2100

Sample proportion of applications were from minority members = = 0.14

Part a) Find the mean of p

Part b) Find the standard deviation of p:

Part c) Find:

Find z score:

Thus we get:

Look in z table for z = -2.5 and 0.00 and find corresponding area.

P( Z <-2.50 ) = 0.0062

thus