You are big lovers of sesame bagels and you wonder if the number of sesame seeds on a bagel follows a normal law. You have counted the number of sesame seeds from 400 randomly selected bagels and you want to perform an adjustment test, at the significance threshold 0.01, to see if the number of sesame seeds on a bagel follows a normal distribution N (? ; ?2) where ? and ? are estimated by = 1300 and s = 275 respectively.a) Use class [1600 ; 1900[ to illustrate the procedure for obtaining the theoretical strength for an adjustment test.b) Perform all the steps of the Khi square test and conclude in the right way (the theoretical frequencies have already been calculated, so no need to recalculate them).

Repartition des 400 bagels selon le nombre de graines de sesame Nombre de Frequencys Frequencys graines de sesame observees theoriques Moins de 700 10 5,9 [700 ; 1000[ 60 49,3 [1000 ; 1300[ 130 144.8 [1300 ; 1600[ 160 144.8 [1600 ; 1900[ 20 1900 et plus 20 5,9 Total 400 400