Question 411555: In a study of elite competitive milers, it was determined that the average time for the mile was 4.00 minutes with a standard deviation of 06 seconds. A friend of yours is training in hopes of becoming an elite miler. Therefore, s/he asked you, as a statistician, to determine the times required to meet the following placements. Answers must be in minutes.
a. The minimum mile time that would place you in the slowest 10%.
b. Between what mile times would place you in the middle 50% of the milers.
c. The mile time that would place you exactly in the middle of the elite milers.
d. The maximum time that would place you in the fastest 10% of the milers.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a study of elite competitive milers, it was determined that the average time for the mile was 4.00 minutes with a standard deviation of 06 seconds. A friend of yours is training in hopes of becoming an elite miler. Therefore, s/he asked you, as a statistician, to determine the times required to meet the following placements. Answers must be in minutes.
a. The minimum mile time that would place you in the slowest 10%.
---
Find the z-value with a left-tail of 10%
invNorm(0.10) = -1.2816
Find the corresponding x-value
x = zs + u
x = -1.2816*0.06 + 4
x = 3.926 minutes
====================================
b. Between what mile times would place you in the middle 50% of the milers.
Use the z-score with a left tail of 25%
Use the z-score with a left tail of 75%
Follow the procedure used in problem "a".
---------------------------------------------
c. The mile time that would place you exactly in the middle of the elite milers.
Find the x-score corresponding to z=0
Ans: 4 minutes
------------------
d. The maximum time that would place you in the fastest 10% of the milers.
Find the z-score with a left-tail of 90%
Then find the corresponding x-value.
===================
Cheers,
Stan H.
=======
|
|
|
