Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 1.3 month.15 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.What is the probability that one randomly selected person learned to walk when the person was between 11 and 13.5 months old? For the 15 people, find the probability that the average age that they learned to walk is between 11 and 13.5 months old. For part b, is the assumption that the distribution is normal necessary? NoYes Find the IQR for the average first time walking age for groups of 15 people. Round to two decimal places.Q1 = monthsQ3 = monthsIQR: months

GivenMean(μ)=12standard deviation(σ)=1.3sample size(n)=151)The probability that one randomly selected person learned to walk when the person was between 11 and 13.5 months old is=P(11<x<13.5)=P(11-μσ<x-μσ<13.5-μσ)=P(11-121.3<z<13.5-121.3)=P(-0.7692<z<1.1538)=P(z<1.1538)-P(z<-0.7692)=0.8757-0.2209 (from excel formula)=0.6548The probability that one randomly selected person learned to walk when the person was between 11 and 13.5 months old is 0.6548 1)For the 15 people the probability that the averageage that the learned to walk is between 11 and 13.5 is=P(11<x<13.5)=P(11-μσn<x-μσn<13.5-μσn)=P(11-121.315<z<13.5-121.315)=P(-2.9792<z<4.4688)=P(z<4.4688)-P(z<-2.9792)=1.0000-0.0014 (from excel formula)=0.9986For the 15 people the probability that the averageage that the learned to walk is between 11 and 13.5 is 0.9986 1)For part b,Yes the assumption of normal is necessary because sample sizeis less than 30The correct answer is Yes1)Q1:-Q1=25th percentileP(z<z0)=0.25P(z<-0.6745)=0.25 (from excel formula) z0=-0.6745x-μσ=-0.6745x-121.3=-0.6745x=12-0.6745(1.3)x=11.12315x≅11.12 monthsQ1=11.12 months Q3:-Q3=75th percentileP(z<z0)=0.75P(z<0.6745)=0.75 (from excel formula) z0=0.6745x-μσ=0.6745x-121.3=0.6745x=12+0.6745(1.3)x=12.87685x≅12.88 monthsQ3=12.88 monthsIQR=Q3-Q1IQR=12.88-11.12IQR=1.76 months