Practice FT2 Q9 - Looking for a detailed, worked solution with theoretical explanation

Members of your local Flat Earth Society meet to examine new photographic evidence that the Earth may actually be hyperbolic and that the horizon has negative curvature. Example Photgraphic Evidence positve curvature (round Earth) zero curvature (flat Earth) negative curvature (hyperbolic Earth) A total of 67 photographs are examined by society members Leo, William and Eugenie, and it is determined that . 17 show the Earth has positive curvature, . 47 show the Earth has no curvature, and . 3 show the Earth has negative curvature. a) Assume that the Earth is flat and that both outcomes (positive or negative) are equally likely. For the sign test, what probability distribution can be used to model the number of photographs with negative curvature? O B (67, ) O B (47, 2 ) O B (20, ) O B (3, 7 ) b) Suppose the random variable X is the number of photographs with negative curvature, with distribution as above. Find . The expected value E(X) = D, and . The variance Var(X) = c) Use a normal approximation with continuity correction, and the table below, to estimate the tail probability that as few as 3 photographs have negative curvature Give your answer to four decimal places, for example as 0. 1234 P(X