A company's orders are classified as coming from geographical area A, B, C, or D. Over a certain period, there were 119 orders from area A. 54 orders from area B. 367 orders from area C. and 115 orders from area D.
(a) It is claimed that the probability that an order is from area A is 0.25, the probability that an order is from area B is 0.10, the probability that an order is from area C is 0.40, and the probability that an order is from area D is 0.25. Are the data consistent with this claim'.'
(b) Construct a two-sided 99% confidence interval for the probability that an order is received from area.