4. Scotes on a standard IQ Test for young adults aged 20 to 34 are normally dist

Question

4. Scotes on a standard IQ Test for young adults aged 20 to 34 are normally distributed 110 and standard deviation 25. You must write the correct notation for probability. You m well labeled, wel-shaded normal curve. If you are using the graphing calculator to with mean must draw a get probabilitie the correct, well-ordered functional notations as given in the graphing calculator Writing only the numerical answer will not get full credits a. What percent of young adults score below 75 on this IQ Test? b. What is the probability that a young adult will score above 180 on this 1Q Test? c What is the probability that a young adult will score between 85 and 160 on this 1Q Test? d Hally only wants to date men in the top 15% on this intelligence scale. How high must a man score for Hally to date him?

Explanation / Answer

The normal distreibution prameters are mean = 110, stdev = 25.

Lets take this to normalize our variable X

a. P(X<75) = P(Z< 75-110/25) = P(Z<-1.4) = .081

b. P(X>1800 = P(Z> 180-110/25) = P(Z>2.5) = 1-.9975 = 0.0026

c. P(85<X<160) = P(85-110/25<Z<160-110/25) = P(-1<X<2) = .97725-0.1587 = 0.819

d. P(X>x) = .15

So, x should be such that Z is 1.035

So, x = Mean + Stdev*Z = 110 + 25*1.035 = 135.875

So, he must score atleast 135.975 to date Hally

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