4. Gender Bias in Promotions: Suppose the probability of selecting a female is 0.3 and the probability of selecting a male is 0.7. Let X denote the number of females selected for promotion in a random sample of 5 employees. Note X follows a binomial distribution. (11 points) a) Find the mean ? and standard deviation ? of X. (Keep 2 decimal points for s.d.) (4) b) What is the probability of having exactly 5 females promoted among the 5 employees? (Keep 3 decimals) (3) c) What is the probability of having more than 3 females promoted among the 5 employees? (Keep 2 decimals) (4)
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The Telektronic Company hired 8 employees from a large pool of applicants with an equal number of males and females. If the hiring is done without regard to sex, the numbers of females hired and the corresponding probabilities are as follows 0(0.004); 1(0.031); 2(0.109); 3(0.219); 4(0.273); 5(0.219); 6(0.109); 7(0.031); 8(0.004) a. Does the given information describe a probability distribution? b. Assuming that a probability distribution is described, find its mean and standard deviation. c. Use the range rule of thumb to identify the range of values for usual numbers of females hired in such groups of eight. d. If the most recent group of eight newly hired employees does not include any females, does there appear to be discrimination based on sex? Explain.
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