Suppose the age that children learn to walk is normally distributed with mean $h$ mentifs und standard deviation 1.3 month. 17 randomly selected people were asked what ave they learned to walk. Round all answers to 4 decimal places where passible What is the probability that one randomly selected person leurned to walk when the persen wis between 11 and 13 months old? For the 17 people, find the probabitity that the ivercere ave that they learned to walk is between 11 and 13 months old

Step 1 ：First, we need to standardize the values of 11 and 13 months to z-scores. The z-score is calculated by subtracting the mean from the value and dividing by the standard deviation. In this case, the mean is $h$ months and the standard deviation is 1.3 months.

Step 2 ：The z-score for 11 months is $z_{11} = \frac{11 - h}{1.3}$ and for 13 months is $z_{13} = \frac{13 - h}{1.3}$.

Step 3 ：The probability that a randomly selected person learned to walk between 11 and 13 months old is the area under the normal distribution curve between $z_{11}$ and $z_{13}$. This can be found by looking up the z-scores in a standard normal distribution table or using a calculator with a normal distribution function.

Step 4 ：Let's denote this probability as $P_{11-13}$. So, $P_{11-13} = P(z_{13}) - P(z_{11})$.

Step 5 ：For the 17 people, we are interested in the average age they learned to walk. The standard deviation of the average of a sample is the standard deviation of the population divided by the square root of the sample size. In this case, the sample size is 17, so the standard deviation of the average is $\frac{1.3}{\sqrt{17}}$.

Step 6 ：We can then standardize the values of 11 and 13 months to z-scores using this new standard deviation. The z-score for 11 months is $z_{11}^{'} = \frac{11 - h}{\frac{1.3}{\sqrt{17}}}$ and for 13 months is $z_{13}^{'} = \frac{13 - h}{\frac{1.3}{\sqrt{17}}}$.

Step 7 ：The probability that the average age that the 17 people learned to walk is between 11 and 13 months old is the area under the normal distribution curve between $z_{11}^{'}$ and $z_{13}^{'}$. This can be found by looking up the z-scores in a standard normal distribution table or using a calculator with a normal distribution function.

Step 8 ：Let's denote this probability as $P_{11-13}^{'}$. So, $P_{11-13}^{'} = P(z_{13}^{'}) - P(z_{11}^{'})$.

Step 9 ：So, the probability that one randomly selected person learned to walk when the person was between 11 and 13 months old is $P_{11-13}$, and for the 17 people, the probability that the average age that they learned to walk is between 11 and 13 months old is $P_{11-13}^{'}$.