Suppose the weight of an adult male German Shepherd is normally distributed with a mean of 36.4 kg and a standard deviation of 4.2 kg. (a) What proportion of adult male German Shepherds will weigh more than 45 kg? (b) What is the probability a randomly selected adult male German Shepherd will weigh between 33 kg and 39 kg? (c) Twenty percent of all adult male German Shepherds have a weight less than what value? (d) Let X represent the average weight of 35 male adult male German Shepherds selected at random. What is the sampling distribution of X ? Explain. (e) What is the probability the average weight of 35 randomly selected adult male German Shepherds will be less than 37.5 kg? (f) If the weights of adult male German Shepherds did not follow a normal distribution, would your answers in parts (d) and (e) still be valid? Explain