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Assume that student marks are normally distributed. A random sample of 25 students' marks yield a sample mean of 70 and a sample standard deviation of 10.
a) Estimate the population mean of marks with 95% confidence.
b) If the population mean of the marks is 67 and the probability that the sample mean of 25 students' marks is greater than 70 is 3%. Find the population standard deviation of the marks.
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