A normal distribution has a mean equal to 45. What is the standard deviation of this normal distribution if 2.5% of the portion under the curve lies to the right of x= 50.88?

Answer 1

The invNorm function on your TI-84 calculator will calculate z score of a certain area (probability). A 2.5% (0.025) portion of the curve to the right equates to 1 - 0.025 or 0.975 to the left. So, if you do invNorm(0.975) it will give you the z score associated with a 97.5% area.

invNorm(0.975) = 1.959964

To turn that z-score into a standard deviation, use the equation for z-score.

z-score = (x - μ)/σ or σ = (x - μ)/Z = (50.88 - 45)/1.959964 = 5.88/1.959964 = 3.000

So the standard deviation is 3.000