19. Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65 and standard deviation
.85 (suggested in Modeling Sediment and Water
Column Interactions for Hydrophobic Pollutants,
Water Res., 1984: 1169—1174).
a. If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.00? Between 2.65 and 3.00?
b. How large a sample size would be required to ensure that the rst probability in part (a) is at least .99?