Question

Please use your knowledge of cumulative distrubution functions (cdfs) and probability mass functions (pmfs) as well as your specialized knoweledge of the normal and binomial distrubutions to answer the following questions

1. At 5'3 (63 inches tall ) tyrone "mugey" borgues ( pictured below next to mamute bol height 7'7 ) in the shortest player in the history of american professsions basket ball . Assume that in the population of american men , height is normally distrubuted with u=69.1 inches and o=2.9

a) calculate an index value for mugsey bogues height and say what this number means in the plain english show your work

b) calculate a z score for mugsey bogues height and say what this number means in plain english. Show your work

c) why is the z score potienally more useful than the index score in characterizing mugsey bogues height

Answer 1

a) The index score is computed as:

63 μ 69.1 _ - 0.9117

The index score basically represents where the player stands with respect to a standard value.

b) The z score for his height is computed as:

63-69. Î 2.9 2. _ μ 92.1034

This in plain english means that the height of the player is 2.1034 standard deviations less than the mean height of all the players.

c) The z score is a more useful measure because it helps to take into account the variation in the data as well.