The pulse rates of 158 randomly selected adult males vary from a low of 44 bpm to a high of 120 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 90​% confidence that the sample mean is within 2 bpm of the population mean. Complete parts​ (a) through​ (c) below. a. Find the sample size using the range rule of thumb to estimate σ.   n=245 ​ b. Assume that σ=10.5 ​bpm, based on the value s=10.5 bpm from the sample of 158 male pulse rates. n=   c.. Compare the results from parts​ (a) and​ (b). Which result is likely to be​ better?

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 + ...