# SOLUTION: find the z score that has 70% of the distribution area to its right

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 Click here to see ALL problems on Probability-and-statistics Question 617157: find the z score that has 70% of the distribution area to its rightAnswer by Edwin McCravy(8882)   (Show Source): You can put this solution on YOUR website!``` The area under the entire normal curve is 1. So the area under each side of the normal curve is .5. We want to find the value of z such that 70% or .70 of the area is under the curve to the right of that z-value. So .50 of the .70 is to the right of z=0 and that leaves .70 - .50 = .20 for the area on the left of z=0. So we look in the body of the normal table and find the nearest value to .20 for the area to the left of z=0 that we need to make up the rest of the 70%. We find that .1985 is the closest area value in the table. Then we observe that .1985 occurs where z = -0.52. We know to take it negative since only negative values of z have more than 60% of the area to the right of them. So that is the value we are looking for. I'll indicate it with a green line at z=-0.52, just a little past halfway between z=0 and z=-1. The area under the curve to the right of the green line at z=-0.52 is 70% of the entire area Edwin```