Question

Variables A and B are normally distributed. Variable A has a mean of 50 and a standard deviation of 10. Variable B has a mean of 80 and a standard deviation of 20. If the probability that A is at or below the number x is 0.20, and the probability that B is at or above the number y is 0.40, what is the value of y – x ?

Answer 1

43.48315

Explanation:

A suitable calculator can compute this number directly. The number used for the inverse CDF function will be p=0.2 for variable A. It will be p=1-0.4 = 0.6 for variable B, because we're concerned about the area in the upper tail for that variable. The first attachment shows the result above:

y - x ≈ 43.48315

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You can also compute the values of x and y individually, then do the subtraction. The second attachment shows x ≈ 41.584; the third attachment shows y ≈ 85.067. Then the difference is ...

y - x ≈ 85.067 -41.584 = 43.483