Solved:
Answered by AI, Verified by Human Experts
A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 ounces with a standard deviation of .2005 ounces. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the means calculated should occur in what interval? Hint: the standard deviation rule says that 95% of the observations are within how many standard deviations away from the mean? Round answers to four decimal places. ( , )
A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 ounces with a standard deviation of .2005 ounces. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the means calculated should occur in what interval? Hint: the standard deviation rule says that 95% of the observations are within how many standard deviations away from the mean? Round answers to four decimal places. ( , )
Using thenormal distribution, it is found that95% of the meanscalculated should occur in(15.8495, 16.2505).In anormal distributionwithmeanandstandard deviation, thez-scoreof ameasure Xis given by:Itmeasureshow many standard deviations the measure is from the mean.After finding the z-score, we look at the z-score table and find thep-valueassociated with this z-score, which is thepercentileof X.TheCentral Limit Theoremstates that for the sampling distribution of sample means of size n, the standard deviation is.TheEmpirical Rulestates that95%of the measures are within 2 standard deviations of the mean, that is,between Z = -2 and Z = 2.In this problem:Meanof 16.05 ounces, thusStandard deviationof 0.2005 ounces, thusSamplesof size 4, thus.95% betweenZ = -2 and Z = 2, thus:Z = -2:By the Central Limit TheoremZ = 2:Interval(15.8495, 16.2505).A similar problem is given atbrainly.com/question/13448290...