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In a survey of 500 U.S. teenagers aged 14 to 18, subjects were asked a variety of questions about personal finance. One question asked whether teens had a debit card. Suppose that exactly 12% of teens aged 14 to 18 have debit cards. Let X = the number of teens in a random sample of size 500 who have a debit card.
1. Explain why X can be modeled by a binomial distribution even though the sample was selected without replacement.
2. Use a binomial distribution to estimate the probability that 50 or fewer teens in the sample have debit cards.
3. Justify why X can be approximated by a Normal distribution.
4. Use a Normal distribution to estimate the probability that 50 or fewer teens in the sample have debit cards.
