Question

for a population of 800000 subway riders, the numbers of subway trips taken per rider last january are approximately normally distributed with a mean of 56 trips and a standard deviation of 13 trips. approximately how many of the riders took between 30 and 43 trips last january???

Answer 1

I hate statistics

Answer 2

me too studyn for my gre

Answer 3

ahhh, zscores, gotta love em

Answer 4

what do you have for computing, table or calculator?

Answer 5

table..and calc on my laptop

Answer 6

\[Z=\frac{x-\mu}{\sigma}\]

Answer 7

we wanna cram the non standard stuff into the normal curve

Answer 8

I neva seen that z formula before

Answer 9

ok

Answer 10

the zscore allows us to compare different amounts as tho they were equals

Answer 11

ok..

Answer 12

so lets start cramming it in :)

mean = 56

30 - 56 = |-26|
43 - 56 = |-13|

and sd = 13, were in luck, your numbers are divisable by 13 so its fairly simple

Answer 13

26/13 = 2, we are 2 standard deviations from the mean

13/13 = 1, we are 1 standard deviation from the mean

the area between 1 and 2 is what we want to find

Answer 14

do you know the "empirical rule"?

Answer 15

ok...so the answers given are
60000
110000
160000
210000
270000

Answer 16

no explain empirical rule..

Answer 17

i got no idea what the answer is yet, I am going thru it along with you :)

Answer 18

the empirical rule is a rule of thumb for the area/probability under the curve for deviations from the mean of 1,2, and 3

Answer 19

1 = 68
2 = 95
3 = 99

but, we need only half of these since our sds are just on one side

Answer 20

2 - 1 will give us the approximate area

95/2 - 68/2 = N

95
-68
----
27 /2 = 13.5 right?

Answer 21

if so then our answer is:

800,000 * .135

Answer 22

.135 * 800000= 108000

looks close to 110000
thanks..

Answer 23

looks good to me, and it makes sense as well :) hope its right ;)

Answer 24

so situations like these i dont necessarily need to draw a bell curve diagam??

Answer 25

draw the curve, its good practice for later

Answer 26

and understand the z score / sds

Answer 27

zscore relates to standard deviations as:

1 zscore: 1 sd

in this problem we are given an sd of 13 so thats a ration of; 1:13, or simply put 1/13

when the mean is at 0 we can equate the distance of any given data point from the mean by using this ratio.

take for instance the data given here:

mean = 56 and we have a distance of 30 away from it;

30 <---->56
-56 -56
---- -----
-26 <----> 0
26

we simply shift it all to look at it at a mean of 0, and an sd of 1, so use our ratio now of 1/13

26*1z/13 = 26z/13 = 2z, we have a zscore of 2, or simply 2 sds away from the mean

Answer 28

not a "distance of 30" but rather we need to find the distance between 56 and 30 ....

Answer 29

ahhhh thankkkkks