Exercise6.7 An accuratecalculationoftheIQ(intelligencelevel) of achildrequiresalongseries of varioustests.Instead,psychologistssuggestanexpressmethodusingalessaccurateintelligence test whoseresult X is relatedtothetrueIQlevel as X

Exercise6.7 An accuratecalculationoftheIQ(intelligencelevel) μ of achildrequiresalongseries of varioustests.Instead,psychologistssuggestanexpressmethodusingalessaccurateintelligence test whoseresult X is relatedtothetrueIQlevel μ as X ∼ N (μ,100). Itisknownthatinthe population asawhole, μ ∼N (100,225). AyoungGeniusgot115inthetest.

1. Find theBayesestimatefortheGenius’IQw.r.t.thesquarederrorand95%HPDsetforit.

2. Genius claimsthathebelongstothegroupofchildrenwithanespeciallyhighIQ(above110).

Testhisclaim.