The honey farm has installed a filling machine for honey jars that hold 500 g of honey. Doris is calibrating the new machine. She sets the machine to a mean of 500 g and performs a test run of 48 jars. Assume it is normally distributed. See the chart below. Honey (G) 499 498 501 498 498 501 497 499 499 502 500 500 501 500 499 500 501 502 501 501 498 500 502 500 498 500 498 500 502 501 500 500 499 500 499 500 496 503 503 499 500 499 501 497 499 502 499 502 Determine the mean of the data Determine the standard deviation of the data. What is the probability that a jar contains at least 504 g of honey? Acceptable jars contain between 496 g and 503 g. What percentage of the jars will be acceptable?
The honey farm has installed a filling machine for honey jars that hold 500 g of honey. Doris is calibrating the new machine. She sets the machine to a mean of 500 g and performs a test run of 48 jars. Assume it is normally distributed. See the chart below. Honey (G) 499 498 501 498 498 501 497 499 499 502 500 500 501 500 499 500 501 502 501 501 498 500 502 500 498 500 498 500 502 501 500 500 499 500 499 500 496 503 503 499 500 499 501 497 499 502 499 502 Determine the mean of the data Determine the standard deviation of the data. What is the probability that a jar contains at least 504 g of honey? Acceptable jars contain between 496 g and 503 g. What percentage of the jars will be acceptable?
The honey farm has installed a filling machine for honey jars that hold 500 g of honey. Doris is calibrating the new machine. She sets the machine to a mean of 500 g and performs a test run of 48 jars. Assume it is normally distributed. See the chart below. Honey (G) 499 498 501 498 498 501 497 499 499 502 500 500 501 500 499 500 501 502 501 501 498 500 502 500 498 500 498 500 502 501 500 500 499 500 499 500 496 503 503 499 500 499 501 497 499 502 499 502 Determine the mean of the data Determine the standard deviation of the data. What is the probability that a jar contains at least 504 g of honey? Acceptable jars contain between 496 g and 503 g. What percentage of the jars will be acceptable?
The honey farm has installed a filling machine for honey jars that hold 500 g of honey. Doris is calibrating the new machine. She sets the machine to a mean of 500 g and performs a test run of 48 jars. Assume it is normally distributed. See the chart below.
Honey (G)
499
498
501
498
498
501
497
499
499
502
500
500
501
500
499
500
501
502
501
501
498
500
502
500
498
500
498
500
502
501
500
500
499
500
499
500
496
503
503
499
500
499
501
497
499
502
499
502
Determine the mean of the data
Determine the standard deviation of the data.
What is the probability that a jar contains at least 504 g of honey?
Acceptable jars contain between 496 g and 503 g. What percentage of the jars will be acceptable?
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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