The heights of a large population of adult females who play basketball are normally distributed with a mean of 175cm and a standard deviation of 7.5cm.
(a) what proportion of this population are less than 2.0m in height?
(b) what proportion of the heights in this population is within 1.4 standard deviation of the mean?
(C) A talent search for potential elite basketball players will do aptitude tests on females in the top 15% of heights.Above what height will females in this population be consider by the basketball talent search?
(d)What proportion of basketball teams(of 5 players) randomly chosen from this population would have an average of more than 182.8cm for its team members?
(e) A visiting basketball coach from an American University was interested in finding tall female basketball players from this population,but was short of time.His approach was to look for basketball teams from the population with team average height above the top 15% height you calculate in (c), and then only interview the tall player within these teams.Use your knowledge of sampling distribution to discuss the advantages and disadvantages of this coach approach as compared to the approach used in (c)