Some psychologists believe that a "genius" should be defined as anyone having an IQ over 140. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, and if the population of the world is 6,575,000,000, how many geniuses are there in the world today?

Question

amistre64 · Answer

so your wanting to find the % of n ..... so find the probability of greater than 140

amistre64 · Answer

z = (x-mean)/sd;  and table it out


or use the normalCDF function on a ti83

anonymous · Answer

I tabled it out and got .9961

amistre64 · Answer

id have to check the table ... :)

40/15 = 2.66666  so thats between 95 and 99.something

anonymous · Answer

ok so what's the next step now

amistre64 · Answer

.9961 are below,  so 1-.9961 are above

amistre64 · Answer

so at 140, left tail is .9961,  right tail has to be .0039

amistre64 · Answer

n*.0039 is the amount of n above 140

anonymous · Answer

so then we multiply .0039 by the total population to find the number of geniuses?

amistre64 · Answer

yep

amistre64 · Answer

if the population is n,  and we determined the percentage ... then n*% is the solution

anonymous · Answer

So i got 25,642,500 when I put it in my calculator but that's not any of the answer choices

amistre64 · Answer

thats correct, but i got no idea what your options are

anonymous · Answer

one of the answers is close but it's off by like a million

anonymous · Answer

A. 24,985,000
B. 536,000,000
C. 123,000
D. 115,000
E. 6,575,000

amistre64 · Answer

id go with the 24.9 then   since its the closest one

anonymous · Answer

alright. thanks for your help!

amistre64 · Answer

yep

dblckd ... z = (140-100)/15 = 2.6666

since its a right tail, your table would give the complement as -2.6666 as well

anonymous · Answer

which comes out as .0039 got it

amistre64 · Answer

http://ucce.ucdavis.edu/files/repository/calag/tab4605p15.jpg even a right tailed table has us at .0039 .... so all signs point to something close to 25m