Question
The forkywisgarosioms are at for pogudation The mean is 68 and the tandard devistion is s A. Cakudate your 2-score-the formuls Iiscore you are wondering abost)-Mimean of the populationill N or l of scores you are 8: 01 the p-eable in yoar toos for Seel free to google ni. fied out what percentage abort. To do this, rou win check the "to, rou er and see what % n componds to Ishould to 4 dipt deernal, and multiply b, 100(10 pt % out of 1001- for instance 8 C Mow woukd your percenlage change if the standard deviation were larger cakculate your new i score and percentage belcw decimal from table D: if thare were 46 kids in your clas, how many of them soored ABOVE you? You now have to tra me data apon what is 7%lthis should be what rougot ror the % in C1 of 46 kids? Multiply the total N by ote original 2 decimal- you catulate the remainder, or 46-cs that scored at or beow kids scored above you not bad niform kids that scored at or below Now to find out how many scored above t: Seeing the difference in the two percentages in A and C, why is standard deviation important? You tried to run a 5K for the first time (ao youl) and ran it in 25 mietes and 15 seconds. The average tisme for Sk runs i& 12 minutes and 3 seconds. The standard deviation is 4.25 minutes. What percentile are you in? ..Hint: you need to transform your time and the average time so there are no seconds left (eg. 25. minutes and 12mintes) & If 1776 people ran the 5K with you, how many did you run the 5K faster than? C: if you ran it in 195 minutes the second time, what percentage of CHANGE is there? "Hint: subtract your original z percentile from your new z percentile
Explanation / Answer
2. t = 25min15sec = 1515 seconds
Mean = 12min3sec = 723 seconds
Stdev = 4.25min = 255 seconds
A.Z = (t-Mean)/stdev = (1515-723)/255 = 3.11
So, P(X<3.11) = 1-.999051 so, I am in the bottom 0.095%
B. 1776*.999051 = 1774.315 ran faster than me 5k. So, I ran faster than 1 person
C. If I ran in 19.5 mins , then percentage change = ?
Znew = (t-Mean)/stdev = (19.5*60-723)/255 = 1.75 which is .9599
So, I am faster than 1776*(1-.9599) = 71.21 or 71 of people
So, the percentage change = .0401 - .00095 = .03915
