Suppose the sediment density of specimens from a certain region has mean 2.55 and standard deviation 0.78.  d) For this part, assume that the sediment density of specimens are normally distributed. What is the probability that the sediment density of a randomly chosen specimen is at most 2.5? Compare your answer with Part c) (answer is .4013) and explain why it is the same or why it is different?     e) For this part, assume that the distribution of sediment density of specimens is unknown. What is the probability that the sample mean sediment density of (independent) random sample of 100 specimens is at most 2.5? Justify why you can use a normal distribution to find the probability.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...