Business and Management In Britain, a small baker does not have a fully automatic plant and sells the majority of his or her production on-site or from vehicles. According to the Birmingham City Council trading standards, the law states that the average weight of one loaf type must be 400 grams. Suppose the Small Baker's Association (SBA) claims that the weight of each loaf of bread of this type is approximately normal with mean 400 grams and standard deviation 15 grams. To check this claim, a random sample of small-baker loaves was obtained, and each was carefully weighed. The observed frequency of weights in each specified interval (in grams) is summarized in the following one-way table.

a. Assume the SBA claim is true. Find the probability that a randomly selected loaf of bread falls into each interval.

b. Use the probabilities computed in part (a) as the hypothesized population proportions associated with each interval. Conduct a goodness-of-fit test to determine whether the observed weights fit the hypothesized distribution. Use a = 0.05. State your conclusion.