In a certain elementary school, 52% of the students are girls. A sample of 65 students is drawn. Would it be unusual for more than 70% of them to be girls? Clearly explain your reason. (Note that your random variable is the sample proportion).

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Mathematics

Kristopher

18 March, 07:15

In a certain elementary school, 52% of the students are girls. A sample of 65 students is drawn. Would it be unusual for more than 70% of them to be girls? Clearly explain your reason. (Note that your random variable is the sample proportion).

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Mia Keith · Answer 1

P = 52% = 0.52

SE = sqrt (p (1 - p) / n) = sqrt (0.52 (1 - 0.52) / 65) = sqrt ((0.52 x 0.48) / 65) = sqrt (0.00384) = 0.0620

Let x be a random variable representing the percent of girls in the sample, then

P (x > 0.70) = 1 - P (x < 0.70) = 1 - P (z < (0.70 - 0.52) / 0.0620) = 1 - P (z < 2.905) = 1 - 0.99816 = 0.00184

The probability that there will be more than 70% of girls in the sample is 0.00184. Therefore, it will be unusual for more than 70% of them to be girls.