According to the American Medical Association, about 36% of all U.S. physicians under the age of 35 are women. Your company has just hired eight physicians under the age of 35 and none is a woman. If a group of women physicians under the age of 35 want to sue your company for discriminatory hiring practices, would they have a strong case based on these numbers? Use the binomial distribution to determine the probability of the company's hiring result occurring randomly, and comment on the potential justification for a lawsuit.

Determine the mean, the variance, and the standard deviation of the following discrete distribution. X P(x) 1 0.223 2 0.303 3 0.186 4 0.151 5 0.137 (Round the intermediate values and final answers to 3 decimal places, e.g. 2.153.) Mean, H = Variance, 62 = Standard deviation, o =Solve for the probabilities of the following binomial distribution problems by using the binomial formula. a. If n = 11 and p = .23, what is the probability that x = 4? b. If n = 6 and p = .50, what is the probability that x 2 1? c. If n = 9 and p = .85, what is the probability that x > 7? d. If n = 14 and p = .70, what is the probability that x s 3? (Round your answers to 4 decimal places.) a. P(x = 4 | n = 11 and p = .23) = b. P(x 2 1 | n = 6 and p = .50) = c. P(x > 7 | n = 9 and p = .85) = d. P(x