In a random sample of 38 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 61 ​months, with a standard deviation of 8 months. Construct and interpret a 95​% confidence interval for the mean length of sentencing for this crime. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Use ascending order. Round to one decimal place as​ needed.) A. 95​% of the sentences for the crime are between ____ and ____ months.   B. There is a 95​% probability that the mean length of sentencing for the crime is between ____ and ____ months.     C. We can be ​95% confident that the mean length of sentencing for the crime is between

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 + ...