Does the average(mean) commuting time in the New York City area differ from the mean commuting time in the Miami, Florid

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Does the average(mean) commuting time in the New York City areadiffer from the mean commuting time in the Miami, Florida area? Themean number of hours, 𝜇x, of weekly commuting inthe New York City area will be compared to the mean number ofhours, 𝜇y of weekly commuting time in theMiami, Florida area. The true valuesof 𝜇x and 𝜇y are unknown.It is recognized that the true standard deviationsare 𝜎x = 3.2 hours for the New York areaand 𝜎y = 2.2 hours for the Miami, Floridaarea. We take a random sample of m = 23 New York commuters and n=39Miami commuters. The mean numbers of hours commuting were x=12.6 for the New York City area and y= 10.3 for the Miamiarea. Assuming all measurements were independent from one anotherand assuming that commuting times are normally distributed we wouldlike to estimate 𝜇x − 𝜇y.
a) What is the standard deviation of the distributionof y?
b) What is the standard deviation of the distributionof x - y ?
c) Create a 95% confidence intervalfor 𝜇x − 𝜇y? (_____ ,_____)
d) What is the length of the confidence interval in part c)?
e) If we let n stay at 39 but vary m, what is the smallest m forwhich the length of the 95% confidence interval would be 2.0 orless?
f) Copy your R script for the above into the text boxhere.