Question

Dans une usine de mise en bouteilles d'eau minerale, il arrive que la machine a etiqueter deteriore les etiquettes. Une etude statistiquwe est realiser afin d'evaluer ce risque avec la machine.. 10 echantillons de 400 bouteilles sont preleves au hasard dand le production. Les effectifs de etiquettes abimees par echantillon sont indiques ci-dedsous:

1 Calculet pour chaque chantillon les frequences a 0'001 qui correspondent aux effectifs obtenues
2 Donner l'étendue de cette serie
3 Donner la fréquence moyenne.

Answer 1

1) To calculate the frequencies at a significance level of 0.001 for each sample, we divide each frequency by the sample size of 400 and then multiply by 0.001.

F1 - 0.04
f2 - 0.01
f3 - 0.025
f4- 0.05
f5- 0.02
f6- 0.045
f7- 0
f8- 0.025
f9- 0.01
F10- 0.015

2) The range of this data set is the difference between the maximum and minimum frequencies. The maximum frequency is 20 and the minimum frequency is 0, so the range is 20 - 0 = 20.

3) The average frequency is the sum of all frequencies divided by the number of samples.

Average frequency = (16 + 4 + 10 + 20 + 8 + 18 + 0 + 10 + 4 + 6) / 10 / 400 = 0.0125

4) An estimate of the probability of a bottle having a damaged label can be obtained from the average frequency calculated in step 3.

Probability of a bottle having a damaged label = 0.0125 = 0.125%

5) If the factory delivers 50,000 bottles to a distributor, the number of damaged labels can be estimated by multiplying the total number of bottles by the estimated probability of a bottle having a damaged label.

Number of damaged labels = 50,000 x 0.0125 = 625