Suppose a variable X is normally distributed with a standard deviation of 10. Given that .0985 of the values of X are greater than 70, what is the mean value of X?

Question

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Answer 1

If 0.0985 is the proportion of data values above 70, then there must be 1-0.0985=0.9015 less than (or equal to) 70, and from tables this corresponds to Z=1.29. Using Z=(X-m)/s where m is the mean and s the standard deviation, m=X-sZ, and m=70-12.9=57.1.