1. a bag contains rubber bands with lengths that are normally distributed with a mean of 6 cm of length, and a standard deviation of 1.5 cm. what percentage of rubber bands can be expected to be shorter than 3 cm?

Roughly 1.7 percent of the bands are shorter than 3cm. We calculate the z score of the data point in standard distribution. By definition of z score, we use score minus mean divided by standard deviation. z=(3-6)/1.5=-2. A z score of -2 corresponds to approximately 1.7%, in other words, roughly 1.7 percent of data is less than 3cm.