Question 953334
yes, it's possible to get a negative z-score.


if your actual score is less than the mean, you will get a negative z-score.


if your actual score is more than the mean, you will get a positive z-score.


if you actual score is the same as the mean, you will get a z-score of zero.


your question is:


the Philadelphia zoo reports that the mean life span of a Galápagos tortoise is 100 years. Assume that their life span follows a normal distribution with the mean = 100 years and standard deviation = 15 years.


a) find the probability that a randomly chosen tortoise will live longer than 70 years. 


the formula for z-score is:


z = (x-m)/s


z is the z-score.
x is the raw score
m is the mean of the raw score
s is the standard deviation of the raw score.


the formula becomes:


z = (70 - 100) / 15 which results in:


z = -2.


you're looking for the probability for having a z-score of -2 or greater.


the z-score of -2 tells you that 2.28% of the area under the normal distribution curve is to the left of that z-score.


this means that 1 - .0228 = .9772 = 97.72% of the area under the normal distribution curve is to the right of that x-score.


this means that the probability that a turtle will live longer than 70 years is equal to 97.72%.


you did good.