The Medical Field of Pediatrics Has Consistently Attracted a Large $\hat{ p}$

Essay

The medical field of pediatrics has consistently attracted a large number of women. The challenge of balancing a personal and professional life is of particular concern to women, and one possible solution is to take a part-time position. A survey of female pediatric residents inquired about the barriers to seeking part-time or reduced-hours employment in the field of pediatrics. Out of 235 women who responded, 153 cited loss of income and 101 cited reduction in benefits as potential barriers.
-Based on what you know about the sampling distribution of $\hat{ p}$ , is it reasonable tothink that this estimate is within 0.05 of the actual value of the population proportion?
Explain why or why not.