Question 1200085
The average sea turtle life span has a normal distribution of 50 years and a standard deviation of 5 years.


1. Find the probability that a sea turtle lives more than 40 years


mean is 50 and standard deviation is 5.


using the z-score calculator at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>, the probability that the turtle lives more than 40 years is equal to .9772.


<img src = "http://theo.x10hosting.com/2023/022203.jpg">


2. Find the IQR.


i believe the Interquartile range is between 25% and 75%, otherwise known as the middle 50% of your values.
using the same z-score calculator used above, the probability of the life of the turtle being in the inter-quartile range is equal to between 46.628 and 53.372.


<img src = "http://theo.x10hosting.com/2023/022204.jpg">


if you work from the z-score, you should get the same answer.


1. Find the probability that a sea turtle lives more than 40 years


z = (x - m) / s
z is the z-score
x is the raw score
m is the raw mean
s is the standard deviation


formula becomes z = (40 - 50) / 5 = -10 / 5 = -2.
area to the left of a z-score of -2 is equal to .0228.
area to the right of that z-score is equal to 1 - .0228 = .9772


<img src = "http://theo.x10hosting.com/2023/022205.jpg">


2. Find the IQR.


you need to find the z-score that has .25 of the area to the left of it and you need to find the z-score that has .75 of the area to the left of it.
the area in between is equal to the larger area minus the smaller area.
z-score that has .25 of the area to the left of it is equal to -.674
z-score that has .75 of the area to the left of it is equal to .674
area in between is .674 minus 



<img src = "http://theo.x10hosting.com/2023/022206.jpg">
<img src = "http://theo.x10hosting.com/2023/022207.jpg">


when z-score = -.674, the z-score formula becomes -.674 = (x - 50) / 5.
solve for x to get x = -.674 * 5 + 50 = 46.63.
when z-score = .674, the z-score formula becomes .674 = (x - 50) / 5.
solve for x to get x = .674 * 5 + 50 = 53.37.
the difference between you got using the raw scores and using the z-scores is do to the valculator rounding.
using my t-84 plus calculator, i got.
.25 area to the left of z-score = -.6744897495.
raw score = 46.628
.75 area to the left of z-score = .6744897495.
raw score = 53.372