Textbook Problem
Water is flowing at a constant rate into a spherical tank. Let V
be the volume of water in the tank and H( t) be the height of the
water in the tank at time t.
(a) What are the meanings of V' (t) and H (1)? Are these derivatives
positive, negative, or zero?
(b) 13 V" (1) positive, negative, or zero? Explain.
(c) Letti ty, and t, be the times when the tank is one-quarter full,
half full, and three-quarters full, respectively.
Are the values H"(t), H"(ty), and H"(ty) positive, negative, or zero?
Why?

Abottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. the water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. a random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon a. construct a 99% confidence interval estimate for the popula-tion mean amount of water included in a 1-gallon bottle. b. on the basis of these results, do you think that the distributor has a right to complain to the water bottling company? why? c. must you assume that the population amount of water per bottle is normally distributed here? explain. d. construct a 95% confidence interval estimate. how does this change your answer to (b)?