The average middle-distance runner at a local high school runs the mile in 4.5 minutes, with a standard deviation of 0.3 minute. Find the percentage of a runners that will run the mile in less than 4 minutes?
A. 45.22%

B. 15.87%

C. 7.15%

D. 4.75%

Question

The average middle-distance runner at a local high school runs the mile in 4.5 minutes, with a standard deviation of 0.3 minute. Find the percentage of a runners that will run the mile in less than 4 minutes? 
 A. 45.22%  
 
 B. 15.87%  
 
 C. 7.15%  
 
 D. 4.75%

amistre64 · Answer

whats the formula to find "z"?

anonymous · Answer

huh ?

amistre64 · Answer

what is your zscore ?

anonymous · Answer

uh idk thats the whole problem

amistre64 · Answer

then you really need to read over the material that corresponds to this question.  they are basic and foundational to the rest of statistics.

anonymous · Answer

i dont have  abook on it or anything its my online schol .

amistre64 · Answer

online schools provide material to study with as well.

amistre64 · Answer

a zscore gives a standard way to equate all the different .... it hard to explain this stuff if you dont have the terminology to relate it to

amistre64 · Answer

it relates all the different spreads that different circumstances can give in order equate them under a usable result

amistre64 · Answer

the zscore measures how far away from the mean a given random variable is.  And that measure relates to the probabilty of the event itself

amistre64 · Answer

to squeeze all the different normal distributions into a zscore that is usabe, we get the mean to zero; so subtract the mean from all the given data points.

x - mean

to relate it to a standard deviation of 1, we divide it by its own standard deviation since sd/sd = 1

z = (x-mean)/sd

you are given a mean of 4.5, an sd of .3, and a point of 4 and less

z = (4-4.5)/.3
   = -.5/.3
   = -1.67

so we would find on the ztable a the place where  1.60  and 0.07  cross

amistre64 · Answer

http://allianthawk.org/images/z_table_positive_bbb.png gives us a ztable we can use

amistre64 · Answer

they cross at 9525, but we are on the wrong side of the mean so we need to adjust this since its actually telling us the amount that is less than 5 ...

10000
-9525
-------
  1475

amistre64 · Answer

forgot how to subtract :)  475

amistre64 · Answer

i know youre not around right now to see this; but I posted it to let you see how important it is to read the material associated with your class before you try to do these kinds of things.  Because they do not get easier along the way

anonymous · Answer

so its 4.75 %?

amistre64 · Answer

yes