Midterm II Study Guide Solutions

Midterm II Study Guide Solutions - Midterm II Study Guide...

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Midterm II Study Guide Solutions 1. Hint: X ~ Binomial Distribution with n=10, and p=0.32 Calculate P(X=5) by binomial prob function (P220) and E(X)=np=3.2 2. Hint: P = 9 claims each week , X=# of claims for one week, X~Poi(9) P(X=7) =9^7 *e^(-9)/7! P(X=0)= 9^0*e^(-9)/0!= e^(-9) (b/c 9^0=1 and 0!=1) P = 9*3=27 claims for 3 weeks, X=# of claims for 3 weeks, X~Poi(27) P(X<4) =P(X=0)+P(X=1)+P(X=2)+P(X=3)=… 3. a) Note: <= means “less than or equal to”, >= means “greater than or equal to” i) P(X>6) = P(Z>(6-7)/0.5) = 1-P(Z<=(6-7)/0.5)=1-P(Z<=-2.0)=1-0.0228= 0.9772 ii) P(7<=X<=8) = P(Z<=(8-7)/0.5) – P(Z<=(7-7)/0.5) = P(Z<=2.0) – P(Z<=0) = 0.9772 - 0.5 = 0.4772 iii) P(6.5<=X<=8.5) = P(Z<=(8.5-7)/0.5) – P(Z<=(6.5-7)/0.5) = P(Z<=3.0) – P(Z<=-1.0) = 0.9986 – 0.1587 = 0.84 b) P(X<7 | X>6) = P(X<7 and X>6)/P(X>6) = P(6<X<7)/P(X>6) P(6<X<7) = P(Z<(7-7)/0.5) – P(Z<(6-7)/0.5) = P(Z<0.0) – P(Z<=-2.0) = 0.5 – 0.0228 = 0.4772 So, P(X<7 | X>6) = 0.4772/0.9772 = 0.4883 4. Let variable X represent test score. 59 percentile corresponds to P(X<x) = 0.59, etc.
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Midterm II Study Guide Solutions - Midterm II Study Guide...

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