What fraction of the population has secure attachment style?
Welcome to Psychology.SE. The answer to your question is not that straight forward. You could have a strong attachment style amongst work colleagues but have an insecure attachment style with superiors or parents.

For different types of attachment (insecure/secure) I would suggest reading the works of John Bowlby who pioneered the theory of attachment.

For further reading there is also a book called Understanding Disorganized Attachment: Theory and Practice for Working with Children and Adults by David and Yvonne Shemmings