Scores on a test are normally distributed with a mean of 68.2 and a standard deviation of 10.4. estimate the probability that among 75 randomly selscted students, at least 20 of them score greater that 78.

First, find the probability of scoring higher than 78. Scores are normally distributed, so you have



Now, the event that any given student scores higher than 78 follows a binomial distribution. Here you have 75 total students (so ) with success probability .

So the probability of getting 20 students that fit the criterion is

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