Example: According to Catalyst, a New York-based women\'s advocacy and research

Question

Example: According to Catalyst, a New York-based women's advocacy and research group, 12% of all corporate officers at the 500 largest U.S. corporations in 1999 were women, compared to 8% in 1995 (Atlanta Journal Constitution, November 12, 1 corporate officers were randomly selected from the 500 largest U.S. firms, what is the probability that none would be women? That half would be women? What is the expected number that would be women? 999.) If eight n-8, p = 0.12, X = # of women P(X = 0) = P(X = 4) =

Explanation / Answer

SOlution:-

n = 8, p = 0.12

a) The probability that none would be women is 0.3596.

x = 0

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 0) = 0.3596

b) The probability that half would be women is 0.0087.

x = 4

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 4) = 0.0087

c) The expected number of women is 0.96.

E(x) = n × p

E(x) = 8 × 0.12

E(x) = 0.96

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