In a study of 100 randomly sampled 18 year-old women in an inner city neighborhood, 15 reported that they were taking birth control pills.

(a) Can the normal approximation to the binomial distribution be used to calculate a confidence interval for proportion of women using birth control pills in this neighborhood? Explain your answer.

(b) Compute an approximate \(95 \%\) confidence interval for the population proportion of women age 18 in this neighborhood taking birth control pills.

(c) Does the interval from part( b) support the claim that, for the young women in this neighborhood, the percentage who use birth control is not significantly different from the national average of 5%? Justify your answer.