It is generally believed that the heights of adult males in the us are approximately normally distributed with means 70 inches ( 5feet, 10 inches) and standard deviation 3 inches and that heights of adult females in the us are also approximately normally distributed with mean 64 inches( 5 feet 4 inches) and standard deviation 2.5 inches. A small university is considering custom ordering the beds for the dorm rooms. Answer the following questions about lengths of beds in dorm rooms at this university. The university plans on ordering custom sized beds such that 99% of male students are expected to fit in them when lying perfectly straight. What length beds should they order? round your answer to the nearest inch.
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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