Question

b) Draw an arrow to show the bin that your soda lies in. Is the volume in your soda unusual? DISTRIBUTION OF INDIVIDUAL SODAS Mean = 12, SD = 0.1 Frequency 73 70 60 59 55 40 39 40 26 20 20 4 0 11.7 11.8 11.9 12 14.1 12.2 12.3 c) Is it unusual for a bottle of soda to contain 11.9 fl.oz.? What makes you think so?

Answer 1

Given Mean = 12, Standard deviation = 0.1

If the bottle of soda contain 11.9 fl.oz, then it is one standard deviation away from the mean to the left of the mean

According to empirical rule or 68-95-99.7% rule, the following % of observations lie within standard deviations of the mean

68-95-99.7 Rule 0.40 0.35 0.30 68.27% 0.25 Probability Density 0.20 95.45% 0.15 0.10 99.73% 0.05 0.00 M - 30 u – 20 H-O и H+ M + 20 u + 30

So from the above image, there are 68.27% observations within one standard deviation of the Mean

So therefore 34.135% of observation lie between Mean and one standard deviation away from the mean to the left or right of the mean

If 34.135% of observation lie between Mean and one standard deviation,  then 15.865% of observation lie below the first standard deviation

So here there are 15.865% of observations that have bottle of soda contain less than 11.9 fl.oz

Hence having a bottle of soda with 11.9 fl.oz is not unusual

In short, there are 15,865% of bottles of soda that contain less than 11.9 fl.oz, which is a signficant number. Hence having a bottle of soda with 11.9 fl.oz is not unusual