The state of Virginia has implemented a Standard of Learning (SOL) test that all public school students must pass before they can graduate from high school. A passing grade is 75. Montgomery County High School administrators want to gauge how well their students might do on the SOL test, but they don€™t want to take the time to test the whole student population. Instead, they selected 20 students at random and gave them the test. The results are as follows:

Assume that SOL test scores are normally distributed. Compute the mean and standard deviation for these data and determine the probability that a student at the high school will pass thetest.

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