One test of extrasensory perception involves the determination of a shape. Fifty blindfolded subjects are asked to identify the one shape selected from the possibilities of a square, circle, triangle, star, heart, and profile of former Prime Minister Paul Martin. Consider as unusual any result that differs from the mean by more than two standard deviations. That is, unusual values are either less than σ - 2σ or greater than µ + 2σ.
a. Assuming that all 50 subjects make random guesses, find the mean and standard deviation for the number of correct responses in such groups of 50.
b. If 12 of 50 responses are correct, is this result within the scope of results likely to occur by chance? What would you conclude if 12 of 50 responses are correct?