Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1.3 month. 17 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.Find the IQR for the average first time walking age for groups of 17 people. Q1 = months Q3 = months IQR: months

Step 1 ：Given that the age that children learn to walk is normally distributed with a mean of 12 months and a standard deviation of 1.3 months. We are asked to find the interquartile range (IQR) for the average first time walking age for groups of 17 people.

Step 2 ：The interquartile range (IQR) is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles, Q3 and Q1. The IQR of a sample is calculated as Q3 - Q1.

Step 3 ：In a normal distribution, the quartiles can be calculated using the z-scores for the 1st quartile (Q1) and the 3rd quartile (Q3). The z-score for Q1 is -0.6745 and for Q3 is 0.6745.

Step 4 ：We can use these z-scores to find the corresponding values in our distribution. The formula to convert z-scores to values in a distribution is X = μ + Zσ, where X is the value in the distribution, μ is the mean, Z is the z-score, and σ is the standard deviation.

Step 5 ：However, since we are dealing with the average of 17 people, the standard deviation of the average would be the standard deviation of the population divided by the square root of the size of the group, which is \(\sqrt{17}\) in this case.

Step 6 ：Calculating the standard deviation of the average, we get \(\sigma_{avg} = \frac{1.3}{\sqrt{17}} = 0.3153\)

Step 7 ：Using the z-scores and the standard deviation of the average, we can calculate Q1 and Q3. For Q1, we get \(Q1 = 12 + (-0.6745)(0.3153) = 11.7873\) months and for Q3, we get \(Q3 = 12 + (0.6745)(0.3153) = 12.2127\) months

Step 8 ：Finally, we calculate the interquartile range (IQR) as \(IQR = Q3 - Q1 = 12.2127 - 11.7873 = 0.4253\) months

Step 9 ：Final Answer: The IQR for the average first time walking age for groups of 17 people is \(\boxed{0.4253}\) months.