Question

A recent study found that fixed fraction, 75%, of a large population of frogs carry a gene for yellow speckled skin.

(a) A sample of 6 frogs is picked at random from this population. Does this qualifies as a binomial experiment (Y or N). Specifically address the 4 requirements and whether each is met or not.

(b) Assume binomial probabilities apply regardless of answer to part a), determine P(X < 6) to 4 decimal places or better. Show all work. Hint: Using complements will take much less work than direct attack.

(c) Find the mean, variance, and standard deviation assuming this is a valid binomial variable. Show calculations.

(d) For bonus (no points loss if you skip as this is section 6.4 which I didn’t cover): Under assumption this is a valid binomail random variable, find the normal approximation for the same probability found in part b. Don’t forget to use continuity correction. You will use mean and standard deviation of part c. Be sure to show calculation for Z-score(s) used.

Answer 1