Philip P. answered • 06/12/21
Affordable, Experienced, and Patient Algebra Tutor
In #1, you got the correct z-scores although the second formula you wrote down should be (43-31)/6 = 2. From the z-score table, the percentile for z = 2 is 0.9772. The percentile for z = -3 is 0.0013. All you have to do now is subtract the lower percentile from the higher one:
P(between 13 and 43) = 0.9772 - 0.0013 = 0.9759
I'm not sure what you did. It looks as if you got the wrong percentile for z = -3 from the table: it should be 0.0013. There is no need to divide by 2. When finding the probability of a score between two other scores, you always subtract the smaller from the larger percentile.
In #2, your z-scores are wrong. The formula is:
z = (x-μ)/σ
which yields:
z = (49-1)/16 = 48/16 = 3
z = (33-1)/16 = 32/16 = 2
Look up the percentiles for z = 3 and z = 2 in a z-score table. Subtract the percentile for z = 2 from the percentile for z = 3 to get the probability of a score between 33 and 43.
Philip P.
If the 0.615 is a z-score, you can look z-score tables up on-line. Just type ";z-score table" in your search box. Most only go to 2 decimal places, so you'll have to interpolate between the percentiles for 0.61 and 0.62.06/12/21
Brian P.
How do I interpolate .375?06/13/21
Philip P.
Halfway between the percentiles for z = 0.37 and 0.38. The percentile for z = 0.37 is 0.6443. The percentile for z = 0.38 is 0.6480. Add them together and divide by two to get the percentile for z = 0.375.06/14/21
Brian P.
I am trying to find the z score for .615, but my table does not include this value. Is there another table that would include this??06/12/21