Question

The results of a race are normally distributed with a mean of 28 minutes and a standard deviation of 4 minutes. The fastest 20% go to districts. Using standard normal probability table, find the 2 probability values which bound the exact probability of finishing in the top 20%

Answer 1

so, i assume you are trying to find the exact minutes?

Answer 2

you are going to have to compare a zscore from a field table ... do you have a table for it?

Answer 3

Yes

Answer 4

Sorry was having trouble responding

Answer 5

do you know how to read the table?

Answer 6

Yes but what values do I look for and if there is an equation how do I set it up?

Answer 7

the table is not going to be exact, but it will give us a field value lower and higher than the exact value ... these define the 'bounds' that they are looking for

Answer 8

there are different tables out there so id have to know what format your table takes.

is it a left tail, a right tail, or a shade from the mean?

Answer 9

.0793 = x - 28/4 ?

Answer 10

It's set up like a multiplication table

Answer 11

IF we knew the exact value, \(\chi\) to begin with, we would use the formula:\[z=\frac{\chi-\mu}{\sigma}\]
this would most likely produce a z score that has more than 2 decimal places to play with; the table most likely only gives us a error rate of 2 decimal places

Answer 12

\[\chi=z(\sigma)+\mu\]
but we cant find an exact z; but can find something a little lower, zo, and a little higher, z1, such that:\[[z_0(\sigma)+\mu]\le \chi\le [z_1(\sigma)+\mu]\]

Answer 13

they are all setup like a multiplication table .... they just have different values depending on how they actually measure the area under the normal distribution curve.

Answer 14

can you show us a picture of your table?

Answer 15

It goes up two decimals on the top and the values have 4 decimal places

Answer 16

sigh ... they all do that. your simply not understanding what im saying about the format of the tables. most likely because youve only seen one format

Answer 17

left tailed format

http://4.bp.blogspot.com/_5u1UHojRiJk/TEh9BHxxPUI/AAAAAAAAAIQ/DafeQNMYFoE/s1600/ztable.gif



right tailed format

http://www.rochester.edu/college/psc/clarke/201/ztable2.jpg



from the mean fromat

http://1.bp.blogspot.com/-X8R15VpvgBI/TuWryLCWR_I/AAAAAAAABZs/1i5yuVpW5oQ/s1600/z-table.jpeg

Answer 18

http://imgur.com/euLhBwE

Answer 19

but regardless of the format, we can know the zscore for 20% left tail of a normal distribution

http://www.wolframalpha.com/input/?i=invnormal%28.2000%29

z = -0.842 ; so your table will most likely have boxed between -0.84 and -0.85

Answer 20

I also need to find the z score in which the most runners will be qualified

Answer 21

nice pic :) yeah, IF we only use that part, then we want to find 1-.2000 = .8000 in the field ... then negate the results since we want the other side of the mean

Answer 22

notice that we can find: .7995 and .8023 in the field; .8000 fits right in between them

Answer 23

so, using the formulas to entrap \(\chi\) we have:

xo = -.84(sd) + mean

x1 = -.85(sd) + mean

Answer 24

as for the second part, im not real sure what "find the z score in which the most runners will be qualified" means for us

Answer 25

i see one typo so far ... since -85 is smaller than -84, i got my xo and x1 mixed up

Answer 26

Thanks is there a special notation needed to write it?