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High school graduates: The National Center for Educational Statistics reported that 82% of freshmen entering public...

High school graduates: The National Center for Educational Statistics reported that 82% of freshmen entering public high schools in the U.S. in 2009 graduated with their class in 2013. A random sample of 135 freshmen is chosen.

c. Find the probability that less than 80% of freshmen in the sample graduated.

d. Find the probability that the sample proportion of students who graduated is between 0.75 and 0.85.

Math   Statistics-And-Probability   
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Answer #1

Since the sample size is large enough, the normal approximation to binomial is used, where the mean and standard deviation of normal distribution are,

c)

The probability that less than 80% of freshmen in the sample graduated is obtained by calculating the z score,

from the standard distribution table,

d)

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