Grades of students in a standard high school exam in Palestine are known to be normally distributed with a mean of $70\mathrm{.}15$ and a standard deviation of $3\mathrm{.}57.$ A random sample of $16$ high school students were taken and their scores in the exam were recorded.

What is the probability that the sample mean is lower than $70\mathrm{.}05?$

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To find the probability that the sample mean is lower than 7005 when the population mean is 7015 and ... View the full answer