normal distribution

[scatteam_2]

the scores on an exam are normally distributed with mean = 30 and s.d= 7

A) wat percent have scores between 30 and 40?
b) what score will place a student in the top 5%?

[DannyN]

i dont remember how to this manually.. but i do know how to do it on a cas calc(ti-nspire) would that be any help?

[Souljette_93]

if you know how to do it in the calc, it should be fine, otherwise you have to look at the Z values.

a) Pr(30<X<40)=Pr(X<40)-(Pr(x<30)

Pr(x<40)=
using Z = (X-mean)/(std dev )
so (40-30)/7=10/7, then look at the Z table for this value. Call this value Z1

do the same with the other one:

(30-30)/7=0  then look for the value in the Z table, call this Z2

so the answer should be Z1-Z2

( sorry, don't have the table with me now, nor do I have a calculator)


part b) they have given you a %. top five means you are looking for a probability of 0.95, now, find this score in the Z table. once you get that, sub it in in the Z formula:

Z=(X-mean)/std dev

You should have the Z, the mean, and Std dev, and now you can find the value of Z.

PS: I'm pretty sure you only use the calculator for this than looking up Z tables. I don't have the answers, but if it's wrong maybe someone can fix it, but that's the general idea

PPS: I think normal distribution should be in methods, not further

[schnappy]

Is this from further or methods? B is readily a further question, but i haven't come across the use of CAS to do normal's such as you would for part A. I've found in further you're expected to use logic (67%-95%-99.7% for sd +1 +2 +3) to find the values, not calculus via CAS.