hmwk10 - ISyE 2027 R. D. Foley Probability with...

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ISyE 2027 Probability with Applications Fall 2006 R. D. Foley Homework 10 November 30, 2006 not due on Tuesday 1. Suppose all trucks heading south on I-24 near Monteagle, Tennesse are inspected before descending the mountain. What would be a reasonable guess as to the distribution of each of the following: (a) the number of trucks inspected until a truck is found with a safety violation? (b) the number of trucks arriving to the inspection facility between midnight and 1 a.m. tonight? (c) the number of trucks that pass the safety inspection out of the first 30 trucks arriving after midnight tonight? (d) the combined weight of the next 15 trucks? (e) the length of time until a Mack truck arrives that is driven by a person named Mack. 2. Suppose Z has a standard normal distribution. Compute (a) Pr { Z 1 . 44 } , (b) Pr {| Z | ≤ 1 . 44 } , (c) Pr { Z > 1 . 44 } , (d) Pr { Z = 1 . 44 } , and (e) find the value of x such that Pr {| Z | > x } = . 05. 3. Suppose X is normally distributed with mean 2 and variance 100. Compute (a) Pr { X 9 } , (b) Pr {| X | > 9 } , and find the value of x such that Pr {| X - 2 | / 3 > x } = . 05. 4. Suppose Y is normally distributed with mean μ and variance σ 2 > 0. Compute Pr { μ - kσ < Y < μ + } for k = 0 , 1 , 2 , and 3. 5. Let Z 1 ,...,Z n be i.i.d. standard normal random variables. It can be shown that if m is an even number, then E[ Z m ] = m ! [2
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hmwk10 - ISyE 2027 R. D. Foley Probability with...

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