Question 953334: Is it possible to get a negative z-zore?
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.
z= 70-100
--------- = -2
15
P(z> -2) 1-0.0228= 0.9772. that's the answer i got but i'm not sure if i did it correctly.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
|
|
|
