Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 134000 dollars. Assume the standard deviation is 30000 dollars. Suppose you take a simple random sample of 82 graduates.
Find the probability that a single randomly selected policy has a mean value between 122736 and 144932.7 dollars.
P(122736 < X < 144932.7) = (Enter your answers as numbers accurate to 4 decimal places.)
Find the probability that a random sample of size n=82 has a mean value between 122736 and 144932.7 dollars.
P(122736 < M < 144932.7) = (Enter your answers as numbers accurate to 4 decimal places.)
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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