SOLUTION: Is it possible to get a negative z-zore? the Philadelphia zoo reports that the mean life span of a Gal�pagos tortoise is 100 years. Assume that their life span follows a normal di

Question 953334: Is it possible to get a negative z-zore?
the Philadelphia zoo reports that the mean life span of a Gal�pagos 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 Gal�pagos 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.

RELATED QUESTIONS
the life span of a battery is normally distributed, with a mean of 2100 hours and a... (answered by stanbon)

9. The life span of a battery is normally distributed, with a mean of 2500 hours and a... (answered by ewatrrr)

the life span of a lynx is about 3/4th the life span of cougar.the average life span of... (answered by josgarithmetic)

Light Bulb Life Span � The life span of a certain type of light bulb is normally... (answered by stanbon)

01. The life span of a battery ins normally distributed with mean 30 months ans standard... (answered by Lightning_Fast)

Sheepdogs have a life span of 8 to 14 years. Calculate the mean and the standard... (answered by Fombitz)

Biologists at the Long Beach aquarium would like to know if conditions at... (answered by stanbon)

A manufacturer claims that the life span of its tires is 51000 miles. You work for a... (answered by Boreal)

"A tortoise crawling at a rate of 0.1mi/h passes a resting hare. The hare wants to rest... (answered by MathTherapy)