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Answer:
a) It is expected that 8 African-Americans get promotions.
b) There is a 8.6% probability that 5 African-Americans get promotions.
c) There is a 16.2% probability that at five or less African-Americans get promotions.
d) The company may be accused of racial discrimination because the ammount of promotions given to African-Americans is much less than expected if there were no discrimination. The expected value, if there is no discrimination, of having more than 5 promotions for African American employees is 84%.
Explanation:
The question is incomplete.
Complete question:
<em>In the workplace, racial 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).</em>
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<em>a) How many African-Americans would you expect to get promotions? </em>
<em> b) What is the probability that five African-Americans receive promotions? </em>
<em> c) What is the probability that five or fewer African-Americans receive promotions? </em>
<em> d) Do you think the company is suspect of racial discrimination? Explain your thinking.</em>
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a) As this situation can be modeled by a binomial distribution B(40,0.2), the expected number of African-Americans that get promotions can be calculated as the expected value of the binomial distribution:
It is expected that 8 African-Americans get promotions.
b) Accordingly to the binomial distribution, we have:
There is a 8.6% probability that 5 African-Americans get promotions.
c) We have to calculate the probabilities for X=0,1,2,3,4 and 5.
There is a 16.2% probability that at five or less African-Americans get promotions.
d) The company may be accused of racial discrimination because the ammount of promotions given to African-Americans is much less than expected if there were no discrimination. The expected value, if there is no discrimination, of having more than 5 promotions for African American employees is 84%.