In 1954, researchers Gollop and Marshall defined age classes of ducks based on their plumage, from the earliest stages "bright ball of fluff," and "fading ball of fluff," to the next-to-last stage "feathered-flightless," and, finally, "flying."26
a. Suppose female mallards at the "bright ball of fluff" stage have weights (in grams) with mean 32.4 and standard deviation 2.4. Find the z-score of a female mallard at this stage that weighs 40 grams.
b. Suppose female mallards at the "fading ball of fluff" stage have weights (in grams) with mean 115.3 and standard deviation 37.6. Find the z-score of a female mallard at this stage that weighs 40 grams.
c. If a female mallard weighs 40 grams, is she more likely to be at the "bright ball of fluff" stage or the "fading ball of fluff" stage? (Base your answer on the z-scores.)