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# Assign4 - STA 3032 Assignment 4 Problem 4.82 a Probability...

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STA 3032 – Assignment 4 Problem 4.82: a.) Probability that requests exceeds the number of rooms (2): 33 . 0 08 . 0 25 . 0 = + b.) Probability that rooms will not be fully utilized: 22 . 0 15 . 0 07 . 0 = + c.) How many rooms are needed so the probability of denying a request 0.10: If one room is added (for a total of three rooms), there will only be a 0.08 probability that a request will be denied on a given day. Problem 4.86: 053 . 0 ) 10 . 0 ( ) 90 . 0 ( ) 10 . 0 ; 7 ( 10 . 0 ) miss Pr( 6 = = = g Problem 4.88: a.) Probability of 18 of 20 have at least 500 hour life: ( 29 2293 . 0 5951 . 0 8244 . 0 ) 85 . 0 , 20 ; 17 ( ) 85 . 0 , 20 ; 18 ( ) 15 . 0 ( 85 . 0 18 20 ) 18 Pr( 2 18 = - = - = = = B B X b.) Probability that at least 15 of 20 have at least 500 hour life: 9327 . 0 0673 . 0 1 ) 14 Pr( 1 ) 15 Pr( = - = - = X X c.) Probability that at least 2 will not have at least 500 hour life: 8244 . 0 ) 18 Pr( = X Problem 4.90: a.) Using definition of expected value: 2 . 1 ) 064 . 0 ( 3 ) 288 . 0 ( 2 432 . 0 ) 216 . 0 ( 0 = + + + = μ b.) Using binomial formula:

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2 . 1 ) 4 . 0 )( 3 ( = = = np μ Problem 4.92: a.) Number of heads in 555 flips of a fair coin. 7792 . 11 ) 5 . 0 )( 5 . 0 )( 555 ( ) 1 ( 5 . 277 ) 5 . 0 )( 555 ( = = - = = = = p np np σ μ b.) Number of 6s in 300 rolls of a fair die.
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Assign4 - STA 3032 Assignment 4 Problem 4.82 a Probability...

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