The length of Atlantic croaker fish are normally distributed, with a mean of 9 inches and a standard deviation of 2 inches. (a) (5 points) If 5 Atlantic croaker fish are randomly selected, find the probability that their mean length is less than 11 inches. (b) (5 points) Suppose we have a random sample of 5 Atlantic croaker fish. What is the value such that 20 percent of the time, the sample mean would be less than this value

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

If c(x) = 4x – 2 and d(x) = x2 + 5x, what is (cxd)(x)

Suppose sat writing scores are normally distributed with a mean of 497 and a standard deviation of 109. a university plans to award scholarships to students whose scores are in the top 2%. what is the minimum score required for the scholarship? round your answer to the nearest whole number, if necessary.