4. A geneticist wants to determine if a gene in fruit flies is sex-linked in such a way that males are more likely to express the trait than females. She does a controlled mating between individuals of known genotypes so that the expected proportion of male offspring that express the trait should be E( P ) = P = 0.25, if the trait is not sex-linked. In her first experiment, the she observes X = 30 out of n = 100 male offspring exhibit the trait ( P = 0.30). a. Describe the sampling distribution of the sample proportion P under the assumption that the trait is not sex-linked. Fill-in the blanks below and scale the X-axis of the accompanying graph. Center: E ( P ): Spread: op: Shape: b. Based on the description of the sampling distribution above, shade the area under the Normal curve in part (a) that corresponds to P [P 2 0.30]. Use the Standard Normal distribution table to determine this probability. . Describe the sampling distribution of P if the student's data were that X=60 out of n =200 male offspring (P =0.30) exhibited the trait (again P = 0.25 if trait not sex-linked). Center: E ( P): Spread: Op: Shape: d. Based on the description of the sampling distribution in part (c), use the Standard Normal distribution table to determine the probability P [P 2 0.30] if P = 0.25. e. What effect did increasing the sample size from n = 100 to n = 200 have on the probability P [ P 20.30 ] if P = 0.25? Explain why you think these probabilities differ