Nicole decides to run for political office. In order for her name to appear on the ballot, she must collect 7,500 valid signatures from registered voters. After she collects 10,000 signatures, she decides to check what proportion of the ones she collected are valid. She takes a random sample of 150 of the signatures she collected and brings them to the Board of Elections to verify them. It turns out that of the sample of 150, only 87 are valid. Construct a 95% confidence interval for the proportion of valid signatures she has collected.