The quality of department of a company tested a bottle of fillers and found them to fill 500 ml bottles to mean of 50.1 ml, with a standard deviation of 0.48 ml. the company’s standard is set at test of results being within two standard deviations of the mean. What is the acceptable range of fill ? if three bottles were tested for fill volume . which are acceptable 501.0 ml, 502.1 ml ,500 ml.
check your typing, 500 ml with a mean of 50.1 ml ??
method
upper = mean + 2(.48) = ..
lower = mean - 2(.48) = ...
To determine the acceptable range of fill, you first need to calculate the upper and lower limits using the given mean and standard deviation.
The upper limit can be calculated by adding two standard deviations to the mean:
Upper Limit = Mean + (2 * Standard Deviation)
The lower limit can be calculated by subtracting two standard deviations from the mean:
Lower Limit = Mean - (2 * Standard Deviation)
Given:
Mean = 50.1 ml
Standard Deviation = 0.48 ml
Calculating the upper limit:
Upper Limit = 50.1 ml + (2 * 0.48 ml)
Upper Limit = 50.1 ml + 0.96 ml
Upper Limit = 51.06 ml
Calculating the lower limit:
Lower Limit = 50.1 ml - (2 * 0.48 ml)
Lower Limit = 50.1 ml - 0.96 ml
Lower Limit = 49.14 ml
Therefore, the acceptable range of fill is between 49.14 ml and 51.06 ml.
To determine which of the three tested fill volumes are acceptable, we need to compare each volume with the acceptable range.
1) 501.0 ml:
This volume is within the acceptable range (between 49.14 ml and 51.06 ml) and is therefore acceptable.
2) 502.1 ml:
This volume is outside the acceptable range (beyond 51.06 ml) and is therefore not acceptable.
3) 500 ml:
This volume is within the acceptable range (between 49.14 ml and 51.06 ml) and is therefore acceptable.
So, out of the three tested fill volumes, the ones that are acceptable are 501.0 ml and 500 ml.