1. Although a particular manufacturer of academic gowns advertises the material of their gowns as being 93% silk, the actual silk content of the gowns varies.  Although the manufacturer’s quality control protocols assure that the mean percentage of silk in the gowns remains at 93%, it is known from experience that the probability of the silk content of any particular gown being between 90% and 95% is 0.9805.  For gowns falling outside that range, the probability that a gown contains less than 90% silk is exactly half the probability that a gown contains more than 95% silk.

Camford University has received an order of 100 gowns from the manufacturer.  It may be assumed that those  gowns represent a random sample.  Let $W$ represent the number of gowns out of those 100 that have a silk content greater than 95%.

Write down the probability distribution that describes $W$.