15. The reaction time X (in minutes) of a certain chemical process follows a Uni

Question

15. The reaction time X (in minutes) of a certain chemical process follows a Uniform Probability Distribution with S S X s 10. What is the probability that the reaction time is between 6 and 8 minutes? 4 B, 05 C. 02 D. Not enough information to find P(6 S X s 8) 16. High temperatures in a certain city for the month of August follow a uniform distribution over the interval 64to 92 F. What is the probability that a randomly selected August day has a high temperatur that exceeded 69 F? 8 A) 0.4423 B) 0.1786 0.8214 D) 0.0357 17, Draw a normal curve with -50 and = 16, Label the mean and the inflection points. B) 18 50 34 50 66 D) 2 50 58 34 50

Explanation / Answer

15)

here for uniform distirbution paramter a =5 and b=10

CDF of uniform distribution =P(X<x)= (x-a)/(b-a) =(x-5)/(10-5) =(x-5)/5

therefore probability of reaction time to be between 6 and 8 =P(6<X<8)=F(8)-F(6)

=(8-5)/5 -(6-5)/5 =0.6-0.2 =0.4

16)

here a =64 ; b=92

hence probability that temperature exceeds 69 =P(X>69)=1-P(X<69)=1-F(69)=1-(69-64)/(92-64)=0.8214

17) as inflection on normal distribution curve falls one std deviation away.

therefore left side inflection point =50-16=34

and right side inflection point =50+14=66

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