A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 83months with a variance of 100.
If the claim is true, what is the probability that the mean monitor life would be less than 81.3 months in a sample of 89 monitors? Round your answer to four decimal places.
Central Limit Theorem with Mean/ don't forget to round
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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A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 8383 months with a variance of 100100.
If the claim is true, what is the probability that the mean monitor life would differ from the population mean by greater than 1.71.7 months in a sample of 8989 monitors? Round your answer to four decimal places.
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