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.

Question

Mathematics

Chasity

29 March, 06:53

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.

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Answers (1)

Know the Answer?

Salvatore Paul · 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