a. What IQ must one have in order to become a member of Mensa?
Let "X=" IQ score: "X\\sim N(\\mu,\\sigma^2)"
Then
Given that "\\mu=100, \\sigma=15"
"0.02=1-P(X<X^*)=1-P(Z<{X^*-100 \\over15})"
"{X^*-100 \\over15}\\approx2.0537"
One must have IQ at least 131 in order to become a member of Mensa.
b. What percent of all Americans have an IQ of at least 145?
"=1-P(Z<3)\\approx0.00135"
Only "0.135\\%" of all Americans have an IQ of at least 145.
c. What percent of all members of Mensa have an IQ of at least 145?
We determine that 2% of all Americans can be the members of Mensa.
We determine that only "0.135\\%" of all Americans have an IQ of at least 145.
Only "6.75\\%" of all members of Mensa have an IQ of at least 145.
d. If Mensa decided to become more exclusive, and accepted only the top 1% instead of the top 2% as members, what IQ would one need in order to become a member of Mensa?
"0.01=1-P(X<X^*)=1-P(Z<{X^*-100 \\over15})"
"{X^*-100 \\over15}\\approx2.32635"
Now one must have IQ at least 135 in order to become a member of Mensa.
Comments
Leave a comment