1. A survey company is asked to estimate the percentage of people in a certain large population that have red hair. Let be the proportion of redheads in the population. The survey decides to take a simple random sample of 1000 people from the population, and use , the proportion of redheads in the sample, as their estimate of .

Find the approximate probability that the absolute value of the error | is less than three percentage points (0.03.)

(Note: The value of p is not given and you may need it in your computation. You could decide one reasonable value to use. Either look for relevant information online or estimate its value in some way. Please justify your option.)