Question

Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1 month. 7 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 X ? X ~ N( , ) What is the distribution of ¯ x ? ¯ x ~ N( , ) What is the probability that one randomly selected person learned to walk when the person was between 10.5 and 12.5 months old? For the 7 people, find the probability that the average age that they learned to walk is between 10.5 and 12.5 months old. For part d), is the assumption that the distribution is normal necessary? YesNo Find the IQR for the average first time walking age for groups of 7 people. Q1 = months Q3 = months IQR: months

Answer 1

a) The distribution of X is normal with mean 12 and standard deviation 1 that is

The distribution of

Define the standard random variable Z as  

So that

Define the standard random variable Z as  

So that

The assumption that the distribution is normal is necessary

Since and

So

and

So IQR is