Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 2 month. 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 N( 11 b. What is the distribution of x? a N( 11 0.3440 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? 0.1389 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 assumptinter an integer or decimal number, accurate to at least 4 decimal places [more..] f. Find the IQR for the average first time walking age for groups of 34 people. Q1 = months Q3 = months IQR: months

Given Information : Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 2 month . 34 randomly selected people people were asked what age they learned to walk . Let, random variable X be the age that children learn to walk . X ~ Normal (μ = 11 , σ = 2) Sampling Distribution of a Normal Variable : Given a random variable X. Suppose that the population distribution of X is known to be normal, with mean µ andvariance σ2 , that is, X ~ N(µ, σ). Then, for any sample size n, it follows that the sampling distribution of X¯ is normal,with mean µ and variance σ 2 /n , that is , X¯ ~ Normal μ,σnFor 34 people , probability that average age that they learned to walk is between 10.6 to 11.3 : n = 34 We need to compute \Pr(10.6 \le \bar X \le 11.3)Pr(10.6≤Xˉ≤11.3). The corresponding z-values needed to be computed are: Therefore, the following is obtained: Probability that average age that they learned to walk is between 10.6 to 11.3 = 0.6873 The first quartile Q1 is the 25th percentile of a data set. The median is the 50th percentile of a data set (also technically the second quartile Q2). The third quartile Q3 is the 75th percentile of a data set. The interquartile range (IQR) is the difference between the third quartile and the first quartile. i.e. IQR = Q3 − Q1 μx¯ = 11 , σx¯=2/34 The first and third quartiles can be found using the mean µ and the standard deviation σ. Q1 = µ − (.675)σ and Q3 = µ + (.675)σ. Quartiles for average first time walking age for group of 34 people : Q1 = μx¯ -0.675σx¯ = 11 - 0.675*0.343 Q1 = 10.7685 Q3 = μx¯ +0.675σx¯ = 11 + 0.675*0.343 Q3 = 11.2315 Hence , IQR = Q3 - Q1 = 11.2315 - 10.7685 IQR = 0.463