The Fresha Tea Company pack tea in bags marked as 250 g
A large number of packs of tea were weighed and the mean and standard deviation were calculated as 255 g and 2.5 g respectively.
Assuming this data is normally distributed, what percentage of packs are underweight?
Answers
Answer:
1) The Fresha Tea Company pack tea in bags marked as 250 g. A large number of packs of tea were weighed and the mean and standard deviation were calculated as 255 g and 2.5 g respectively. The weights of newborns are normally distributed.
2.5%
Given:
The data is assumed to be normally distributed, with a mean of 255 g and a standard deviation of 2.5 g.
To find:
what percentage of packs are underweight?
Solution:
Because we have a normal distribution curve, one standard deviation below the mean equals 252.5 g, one standard deviation above the mean equals 257.5 g, two standard deviations below the mean equals 250 g, and two standard deviations above the mean equals 260 g. 247.5 g is three standard deviations below the mean, and 262.5 g is three standard deviations above the mean.
According to the empirical rule, 68% of the data are within one standard deviation of the mean, 95% are within two standard deviations of the mean, 99.7% are within three standard deviations of the mean, and 0.3% are outside the three standard deviations of the mean. The bell curve below illustrates this.
As a result, the percentage of packs that are underweight is 2.35% + 0.15% = 2.5%.
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