The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.   For a sample of n=60​, find the probability of a sample mean being less than 21.8 if μ=22 and σ=1.35.   LOADING... Click the icon to view page 1 of the standard normal table. LOADING... Click the icon to view page 2 of the standard normal table.       Question content area bottom Part 1 For a sample of n=60​, the probability of a sample mean being less than 21.8 if μ=22 and σ=1.35 is enter your response here   . ​(Round to four decimal places as​ needed.) Part 2 Would the given sample mean be considered​ unusual?   The sample mean ▼   would not would be considered unusual because it has a probability that is ▼   less greater than​ 5%.

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 + ...