4(16 pts). Weights of female cats of a certain breed are normally distributed with mean = 4.0 kg and standard deviation 0.55 kg. Let X be the weight of a randomly selected female cat. = (a) What is the proportion of female cats have weights between 3.8 kg and 4.3 kg? i.e., P(3.8 X 4.3). (b) A certain cat has a weight that is 0.7 standard deviation (i.e. 0.70) above the mean . What is the proportion of female cats that is heavier than this one? i.e., P(X +0.80). (c) How heavy is the female cat whose weight is on the 90th percentile? i.e., P(X) = 0.90 where xo is the value of 90th percentile of the female cat. (d) A sample of 16 female cats is selected at random. What is the probability that mean weight X, is more than 4.3 kg?