P Hat Probability Problem: proportion of girls that play more than one sport is...

Captain12

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According to researchers the proportion of girls that play more than one sport in high school is 82%. Coach Hayes was interested if this was true for her school. Out of a sample of 50 girls randomly selected she is interested in the probability that more than 70% of them play more than one sport. Find that probability. Round your answer correctly to four decimal places.

I don't get what to do.

 
I would interpret the problem as "assuming that 82% of the girls in the school play more than one sport, what is the probability that "in a sample of 50 girls, at least 35 girls (70% of 50) play more than one sport". I would treat this as a binomial probability with "plays more than one sport" having probability 0.82 and "does not play more than one sport" having probability 0.18.

The sample size is large enough that you should be able to use the normal approximation to the binomial distribution.
 
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