The weight of an orange follows a normal distribution with mean 4.0 oz and standard deviation 1.0 oz.
a) Find the probability that a randomly selected orange has weight less than 3.7 oz.
b) Find the probability that the mean weight of 100 oranges is less than 3.7 oz.
c) If you sample 100 oranges and find that sample mean weight to be 3.7 oz, would you doubt the statement that the orange comes from the population with mean weight of 4.0 oz and standard deviation of 1.0 oz? Justify your answer.