SOLUTION: Mensa is an organization whose members possess IQ that are in the top 2% of the population. It is given that IQs are normally distributed with a mean of 100 and a standard deviati

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Question 1175196: Mensa is an organization whose members possess IQ that are in the top 2% of the population. It is given that IQs are normally distributed with a mean of 100 and a standard deviation of 15.
(a) Find the proportion of people having IQ between 85 and 109.
(3 marks)
(b) Find the minimum IQ needed to be a Mensa member. (4 marks)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Normal Distribution:   μ = 100   σ = 15
Using TI Calculator or similarly one like a Casio fx-115 ES plus:
P( 85 < x < 109) = normalcdf(85,109,15,100) =.5671  0r 56.71%

'Highly recommend' using a Calculator when working with Normal Distributions.
w/o recommend checking one's calculations with online sources such as stattrek.com 
0r keisan.casio.com has great illustrations, as Shown below.

Note: | z+=blue+%28x+-+mu%29%2Fblue%28sigma%29 and curve continuous
P(85< x <109) = P(x ≤ 109) - P(x ≤ 85) = P(z ≤ 9/15) - P(z ≤ -15/15) 
  .

b) top 2% (1-.02 = .98) z = 2.0537   &  x = z*σ +  μ 
 x = 2.0537*15 + 100 = 130.806
Or 
Using TI Calculator or similarly one like a Casio fx-115 ES plus:
P(top 2%) = invNorm(.98,15,100) = 130.806
  131  the minimum IQ needed to be a Mensa member. 
                                                                                                                                                                                                                                                                                                                                                                                                                                                               
Wish You the Best in your Studies.