weer dat die nuwe presies 440 ml Volgens die dat die volume alverdeel is met ' \( n \) vyking 12. dat ' \( n \) ewekansige 430 ml koeldrank [2] dat die gemiddelde ekansige steekproef fll en 442 ml sal [3] [4] gebruik om ' n sekere ospitaal is 300 mense A toegedien, maar \( 0 \% \) vertrouensinterval mense, met hierdie A worker at Coocoo-Cola claims that the new "Buddy" Coocoo bottles don't hold exactly 440 ml of soft drink. According to the manufacturing process, he knows that the volume of soft drink in the bottles is normally distributed with mean 440 and standard deviation 12. 6.1 What is the probability that a randomly chosen bottle contains less than 430 ml of soft drink? [2] 6.2 What is the probability that, for a random sample of 49 bottles, the mean volume of soft drink is between 436 ml and 442 ml ? [3] Question 7 [4] Treatment A is used at hospitals to cure a certain disease. At one specific hospital, 300 people with this disease are given Treatment A, but only 267 of them are cured. Determine a \( 90 \% \) confidence interval for the population proportion of people, with this disease, who
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The Deep Dive
Die waarskynlikheid dat 'n ewekansige bottel minder as 430 ml koeldrank bevat, kan bereken word deur die normale verspreiding te gebruik. Met 'n gemiddelde van 440 ml en 'n standaardafwyking van 12 ml, kan ons die Z-skuif gebruik: \( Z = \frac{X - \mu}{\sigma} \). Hier is \( X = 430 \), \( \mu = 440 \), en \( \sigma = 12 \). Dit gee 'n Z-waarde van ongeveer -0,83, wat 'n waarskynlikheid van ongeveer 0,2033 of 20,33% beteken. Vir die tweede vraag, om die waarskynlikheid te bereken dat die gemiddelde volume van 49 flessies tussen 436 ml en 442 ml lê, gebruik ons die standaardfout van die gemiddelde (SEM). Die SEM is \( \frac{\sigma}{\sqrt{n}} = \frac{12}{\sqrt{49}} = \frac{12}{7} \approx 1,71 \). Bereken die Z-waardes vir 436 ml en 442 ml sodat jy die waarskynlikhede kan vind. Dit sal lei tot 'nтеңende waarde tussen ongeveer 0,1587 en 0,8413, wat jou die totale waarskynlikheid sal gee.