Question

In the workplace rascial discrimination is a very serious issue. consider a company in which 20% of the employees are African-American. At the end of the year, promotions are awarded to a group of employees. Out of the 40 promotions awarded, five are African-American. Given that the awarding follows the binomial distribution, B(40,.2).

a) How many African-Americans would you expect to get promotions?
b) What is the probability that five African-Americans receive promotions?
c) What is the probability that five or fewer African-Americans receive promotions?
d) Do you think the company is suspect of racial discrimination? Explain your thinking.

Answer 1

a) How many African-Americans would you expect to get promotions?

Since we have been asked to follow the binomial distribution, (B (40,0.2)

To calculate the mean of the BPD = n*p

where n is the number of promotions and p = probability

= 40 x 0.2 = 8

You expect 8 promotions.

b)

The probability that 5 African-Americans = P (X = 5)

P( X = 5 ) = 40 sqr root ( 5 * 0.2^5 * 0.8^35 ) = 0.0854

c) What is the probability that five or fewer African-Americans receive promotions?

P( X <= 5) = P(X=5) + P(X=4) + ... + P(X=1) + P(X=0)

faster way is calculator

binomcdf(40, .2, 5) = 0.1613

Explanation: