Suppose the age that children learn to walk is normally distributed with mean 13 months and standard deviation 1 month. 9 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected person learned to walk when the person was between 11.5 and 14 months old?  For the 9 people, find the probability that the average age that they learned to walk is between 11.5 and 14 months old.  For part d), is the assumption that the distribution is normal necessary? NoYes Find the IQR for the average first time walking age for groups of 9 people. Q1 =  months Q3 =  months IQR:  months

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 + ...