The ages of the winners of a cycling tournament are approximately​ bell-shaped. The mean age is 27.3 ​years, with a standard deviation of 3.4 years. The winner in one recent year was 26 years old.   ​(a) Transform the age to a​ z-score. ​(b) Interpret the results. ​(c) Determine whether the age is unusual.     (A) Transform the age to a​ z-score. z= ​(Type an integer or decimal rounded to two decimal places as​ needed.)     (B) Interpret the results.   An age of 26 is about= standard​ deviation(s) ▼ A.belowbelow B.aboveabove C.the mean. ​(Type an integer or decimal rounded to two decimal places as​ needed.)     ​(C) Determine whether the age is unusual. Choose the correct answer below.     A. No, this value is not unusual. A​ z-score outside of the range from −2 to 2 is not unusual.   B. Yes, this value is unusual. A​ z-score between −2 and 2 is unusual.   C. No, this value is not unusual. A​ z-score between −2 and 2 is not unusual.   D. Yes, this value is unusual. A​ z-score outside of the range from −2 to 2 is unusual.

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 + ...