 Arraryeldergox2

2022-06-25

I was given a question where I was supposed to find the probability of obtaining y between two scores, however when I input my answer it tells me that I'm wrong, the question is given below along with my answer to the question:

Question
For a normal distribution with sample mean =−19 and standard deviation =6.85 find $p\left(-16.15\le y\le -15.27\right)$, where y is a random draw from the normal distribution. Round to 4 decimal places.

I obtained the z scores for both the y values −15.27 and −16.15 and their respective z scores are 0.5445 and 0.4161. The probability under the curve with a z score of 0.5445 is 0.7054 and the probability under the curve with a z score of 0.4161 is 0.6628. With those two probabilities, I obtained the difference (getting 0.0426) and I put in that answer and was told that I was wrong. Can someone give me insight as to what I'm doing wrong? Alisa Gilmore

The problem is your CDF table for the normal distribution only allows you to get a couple decimals, so you're saying $\mathrm{\Phi }\left(.5445\right)\approx \mathrm{\Phi }\left(.54\right)=.7054$ which (apparently) isn't a good enough approximation.
$\mathrm{\Phi }\left(.5445\right)-\mathrm{\Phi }\left(.4161\right)\approx .706951-.661332=.045619\approx .04562$ Bailee Short