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Category > Statistics Posted 08 May 2017 My Price 5.00

Peter and Paul agree to meet at a restaurant at noon

 

Peter and Paul agree to meet at a restaurant at noon. Peter arrives at a time normally distributed with mean 12:00 noon, and standard deviations 5 minutes. Paul arrives at a time normally distributed with mean 12:02 P.M. and standard deviation 3 minutes Assuming the Two arrival times are independent, find the chance that

a)      Peter arrives before Paul:           b) both mean arrive within 3 minutes of noon:

b)     The two men arrive within 3 minutes of each other.

 

 
 

Answers

Alpha Geek
(8)
Status NEW Posted 08 May 2017 04:05 PM My Price 5.00

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file 1494261846-2245229_1_636297428928670151_2245229.docx preview (71 words )
(-----------a) -----------Let----------- X----------- an-----------d Y----------- r-----------epr-----------ese-----------nt -----------tim-----------es -----------whe-----------n P-----------ete-----------r a-----------nd -----------Pau-----------l a-----------rri-----------ve,----------- re-----------spe-----------cti-----------vel-----------y. -----------We -----------can----------- ta-----------ke -----------noo-----------n t-----------o b-----------e t-----------he -----------ori-----------gin----------- of----------- th-----------e c-----------oor-----------din-----------ate----------- sy-----------ste-----------m a-----------nd -----------the-----------n -----------X a-----------nd -----------Y a-----------re -----------nor-----------mal----------- (0-----------,25-----------) a-----------nd -----------nor-----------mal----------- di-----------str-----------ibu-----------tio-----------ns,----------- re-----------spe-----------cti-----------vel-----------y. -----------Usi-----------ng -----------the----------- fo-----------rmu-----------la -----------for----------- a -----------lin-----------ear----------- co-----------mbi-----------nat-----------ion----------- of----------- no-----------rma-----------l v-----------ari-----------abl-----------es,----------- we----------- o-----------bta-----------in -----------tha-----------t (-----------X â-----------ˆ’Y-----------) i-----------s a----------- no-----------rma-----------l (-----------2, -----------34)----------- di-----------str-----------ibu-----------tio-----------n. -----------Thu-----------s t-----------he -----------pro-----------bab-----------ili-----------tyÂ----------- th-----------at -----------Pet-----------er -----------arr-----------ive-----------s b-----------efo-----------re -----------Pau-----------l i-----------s -----------P(X----------- &-----------amp-----------;lt-----------; Y-----------) -----------=P -----------(X -----------−-----------Y &-----------amp-----------;lt-----------;0)-----------
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