Suppose the age that children learn to walk is normally distributed with mean 13 months and standard deviation 1.4 month. 10 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.
a. What is the distribution of
b. What is the distribution of $\bar{x}$ ? $\bar{x}-\mathrm{N}$
c. What is the probability that one randomly selected person learned to walk when the person was between 12 and 14.5 months old?
d. For the 10 people, find the probability that the average age that they learned to walk is between 12 and 14.5 months old.
e. For part d), is the assumption that the distribution is normal necessary? Noo Yes os
f. Find the $I Q R$ for the average firt time walking age for groups of 10 people.
\[
\begin{array}{l}
\mathrm{Q} 1=\square \text { months } \\
\mathrm{Q} 3=\square \text { months } \\
\text { IQR: } \square_{\text {months }}
\end{array}
\]
IQR: months
Answer
\(\boxed{\text{Final Answer: The distribution of the age that children learn to walk is a normal distribution with a mean of 13 months and a standard deviation of 1.4 months.}}\)
Step 1 ：The problem states that the age that children learn to walk is normally distributed with a mean of 13 months and a standard deviation of 1.4 months.
Step 2 ：We are asked to find the distribution of this data.
Step 3 ：Since the data is normally distributed, we can describe the distribution using the mean and standard deviation.
Step 4 ：The mean of the distribution is 13 months, and the standard deviation is 1.4 months.
Step 5 ：Therefore, the distribution of the age that children learn to walk is a normal distribution with a mean of 13 months and a standard deviation of 1.4 months.
Step 6 ：\(\boxed{\text{Final Answer: The distribution of the age that children learn to walk is a normal distribution with a mean of 13 months and a standard deviation of 1.4 months.}}\)
