Travel and transportation - lighthouses are constructed to guide ships traveling in rocky waters and to allow sailing at night. there are many ways to descrive the size of a lighthouse. however, the height is usally measured from the base of the tower to the top of the ventilator ball. a random sampel of 18 lighthouses in france and england was obtained, and the height of each was recorded. the sample mean was x? = 33.75 meters. assume the distribution of the lighthouse heights is normal and ? = 5.4 meters.

a. find a 95% confidence interval for the mean height of all lighthouses in france and england.

b. how large a sample is necessary to ensure that the width of the resulting 95% condifence interval is 2 meteres?

c. why is the confidence interaval constructed in part(a) valid even though the sample size n = 18 is less than 30?