The advertised fuel economy of the 2020 Toyota Camry model with 4 cylinders and a 2.5 liter engine is 34 miles per gallon (mpg). The observed fuel economy among drivers of that vehicle is slightly lower. The distribution of those values is approximately normal with a mean mpg is 33.5. When a model of this vehicle is randomly selected, the probability that its mpg is 2.8 standard deviations above the mean is 0.39. Find the probability a randomly selected model of this vehicle has mpg 2.8 standard deviations below the mean. Express the answer as a decimal value rounded to the nearest hundredth.
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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 + ...
Expert Solution
Consider,
X = fuel economy among drivers of that vehicle.
The distribution of those values is approximately normal with a mean mpg is 33.5
i.e X has Normal distribution with
mu = 33.5 and sigma is not given.
We have also given that,
When a model of this vehicle is randomly selected, the probability that its mpg is 2.8 standard deviations above the mean is 0.39
&
we have to find the probability a randomly selected model of this vehicle has mpg 2.8 standard deviations below the mean.
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