$Z$ score probability

Question

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 $p( -16.15 \leq y \leq -15.27 )$, where $y$ is a random draw from the normal distribution. Round to $4$ decimal places.

My answer
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?

Answer 1

The problem is your CDF table for the normal distribution only allows you to get a couple decimals, so you're saying $\Phi(.5445) \approx \Phi(.54) = .7054$ which (apparently) isn't a good enough approximation.

$\Phi(.5445)- \Phi(.4161) \approx .706951 - .661332 = .045619 \approx .04562$

I found these values using Wolfram Alpha.

Answer 2

You should state what type of technology you are allowed to use. If you use a regular CAS-enabled calculator and plug in the command: normCdf(-16.15,-15.27,-19,6.85) meaning: Dear Calculator, please tell me the probability for a normal distribution with a mean of -19 and standard deviation 6.85 that a random draw from the normal distribution lies between -15.27 and -16.15.

You should get the value 0.046

Not sure what your mistake is and, I am not sure what you mean by the probability under the cureve with a z-score of 0.4161, since the probability of a certain z-score is always 0.

Answer 3

You haven'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.