3. The weight of fish in Baggins Creek have a mean of 5 pounds and a standard deviation of 1.25 pounds. You catch a random sample of 36 fish and compute their mean weight. (a) What are the values of the mean and the standard error of the mean for this sampling distribution of the mean? (b) What is the probability that the sample mean falls between 5.3 and 5.6 pounds? (c) Find a weight such that the probability that the sample mean falls above it is 30%. (d) What is the probability that the sample mean is less than 4.5 pounds? (e) Find two weights symmetric about the mean such that the probability that the sample mean falls between them is 90%. (f) Why are we justified in assuming that the sampling distribution of the mean will be normally distributed in this problem? Answer d, e, f please
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 + ...
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