b. What is the distribution of x? ¤ - N( c. What is the probability that one randomly selected person learned to walk when the person was between 10.6 and 11.3 months old?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 2 months. 34 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 \( X \)?
\[ X \sim N(\_\_\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_\_\_) \]
b. What is the distribution of \( \bar{x} \)?
\[ \bar{x} \sim N(\_\_\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_\_\_) \]
c. What is the probability that one randomly selected person learned to walk when the person was between 10.6 and 11.3 months old?
\_\_\_\_\_\_\_\_\_\_
d. For the 34 people, find the probability that the average age that they learned to walk is between 10.6 and 11.3 months old.
\_\_\_\_\_\_\_\_\_\_
e. For part d), is the assumption that the distribution is normal necessary?
[ ] No [ ] Yes
f. Find the IQR for the average first time walking age for groups of 34 people.
Q1 = \_\_\_\_\_\_\_\_\_\_ months
Q3 = \_\_\_\_\_\_\_\_\_\_ months
IQR: \_\_\_\_\_\_\_\_\_\_ months](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef4421a9-80f4-44ac-a84c-7924c290e1b7%2F7588e4c9-1104-4747-89b9-7355d8bf266c%2Ftxgm3h_processed.jpeg&w=3840&q=75)
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