# Normal Distribution and Joint Probability Distribution

54. 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 Research, 1984: 1169?1174).

a. If a random sample of 25 specimens is selected, what is the probability 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 the the first probability in part (a) is at least .99?

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Solution. a) If the population follows normal distribution with mean 2.65 and standard deviation 0.85. Then for a sample ...

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Normal Distribution, Joint Probability Distribution and Random Samples are investigated. The solution is detailed and well presented.