USE THIS INFORMATION TO ANSWER QUESTIONS 12-14. An industrial mad pump cleanse h

Question

USE THIS INFORMATION TO ANSWER QUESTIONS 12-14. An industrial mad pump cleanse hine is known to ate that can-be described by the uniform distribution over the RK into a process at a r erval 5.5 to 9.5 gallons per minute. Find each probability. FOR FULL CREDIT SHOW WO Find the probability that more than 8 gallons per minute are released. (3 points) 12. Find the probability that at most 6 gallons per minute are released. (3 points) 13. Find the probability that between 8.5 and 10.5 gallons per minute are released. 14. (3 points) Tur EORMUL A AND WORK FOR FULL CREDIT.

Explanation / Answer

here for uniform distribution paramter a =5.5 and b=9.5

therefore CDF =P(X<x) =(x-a)/(b-a)=(x-5.5)/(9.5-5.5)=(x-5.5)/4

12)P(X>8)=1-P(X<8)=1-(8-5.5)/4=0.375

13)P(X<6)=(6-5.5)/4=0.125

14)P(8.5<X<10.5)=P(8.5<X<9.5)=(X<9.5)-P(X<8.5)=(9.5-5.5)/4-(8.5-5.5)/4=0.25

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