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:QuestionFor a normal distribution with sample mean =−19 and standard deviation =6.85 find p ( − 16.15 ≤ y ≤ − 15.27 ), where y is a random draw from the normal distribution. Round to 4 decimal places.My answerI 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?

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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&#039;m wrong, the question is given below along with my answer to the question:QuestionFor a normal distribution with sample mean =−19 and standard deviation =6.85 find   p  (  −  16.15  ≤  y  ≤  −  15.27  ), where y is a random draw from the normal distribution. Round to 4 decimal places.My answerI 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&#039;m doing wrong?

Alisa Gilmore · Accepted Answer

The problem is your CDF table for the normal distribution only allows you to get a couple decimals, so you&#039;re saying   Φ  (  .5445  )  ≈  Φ  (  .54  )  =  .7054 which (apparently) isn&#039;t a good enough approximation.  Φ  (  .5445  )  −  Φ  (  .4161  )  ≈  .706951  −  .661332  =  .045619  ≈  .04562

Bailee Short · Accepted Answer

You haven&#039;t maintained enough numerical precision. Specifically, it looks like you rounded your z-scores to two significant figures. Your result is the probability of a z-score between 0.42 and 0.54, not between 0.4161 and 0.5445.

I was given a question where I was supposed to find the probability of obtaining y between two score

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