James B. answered • 03/17/23
B.S. in Math with 2+ years tutoring experience
To do this problem you need to look up a z-score table (just google 'z-score table' and click the first result) since I'm pretty sure that's what the 'z' is referring to in your question.
A z-score is the number of standard deviations away from the mean that you are in the standard normal distribution. Thus the greater the value of z the further you away you are from the mean, which has the greatest concentration of values, and the probability of obtaining such z-scores is lower and lower.
In the z-score table the value corresponding to a z-score of -2.89 is .0019. the value corresponding to a z-score of -2.7 is 0.0035. What these values mean is that 0.19% of all values in the standard normal distribution are to the let of this z-score, and thus the -2.7 z-score means 0.35% of all values are to the let of that z-score. That is the 'area under the curve' past z = -2.89 is 0.0019 and 0.0035 past z = -2.7.
Thus to get the answer to your question we just subtract the probabilities, 0.0035 - 0.0019 which returns 0.0016 or a 0.16% probability to get values between -2.89 and -2.7.
