After searching the internet for a way to add scroll bars to a block view in Drupal 7 it turns out to be rather simple.

Under advanced settings in veiws there is setting for CSS class.  So I added a class to div in my custom css file for my theme.  See https://www.drupal.org/docs/7/theming/working-with-css for more details about css in drupal 7.

The following classes were added:

/* Add scroll bars; define a set height for the divl and add
 * a medium height for over riding the set heght
 */

div.outer {
    height: 220px;
    overflow: auto;    
    }
div.medheight {
    height: 350px;
    }

The div.outer will have a block height of 220px and scroll bars if the content overflows.  The div.medheight can be used to override the height, setting it at 350px

Now in view Advanced -> CSS class setting add "outer" and if needing 350px height "medheight".

Save and clear cache and adjust heights if needed.