A random digit dialing poll was conducted, and participants were asked the following question: "Do you personally enjoy the work of artist Van Gogh?" (All respondents answered either "yes" or "no".)

If in the entire inhabitants, the true proportion of people who would answer "yes" is 0.55, what is the probability that the sample mean would be less than 0.5in a sample of 200 people?

0.078 is the answer- please explain