Tubs of natural yogurt are labeled as weighing 1000g. Surveys found the weights to be normally distributed with a mean of 1022g and a standard deviation of 11g. What percentage of the tubs contain more than the labeled weight?
First, complete the labels of the bell curve by using the mean and standard deviation.
For example, start with the mean, 1022g. Then add and subtract 11g to get the values 1 standard deviation above and below the mean.
Keep adding and subtracting the standard deviation until the labels are completed.
We are asked about the percentage of tubs that weigh more than the labeled weight, which is 1000g.
In the curve, this means we are looking for the percentage from 1000 onwards.
All the data above the mean (1022) is 50%
Knowing that 95% of the data lies 2 SDs below and above the mean, we can say that the data between 1000 and 1022 is 2 SDs just below the mean.
Compute for the final percentage.
50%+95%2
=50%+47.5%
=97.5%
The percentage of the tubs that weigh more than the labeled weight is 97.5%.
97.5%
Question 2 of 4
2. Question
Tubs of natural yogurt are labeled as weighing 1000g. Surveys found the weights to be normally distributed with a mean of 1022g and a standard deviation of 11g. If there are 4000 tubs included in the survey, how many contain less than the labelled weight?
We are asked about how many tubs weighed less than 1000g.
First, we find the percentage of these tubs.
All the data below the mean (1022) is 50%.
Knowing that 95% of the data lies 2 SDs below and above the mean, we can say that the data between 1000 and 1022 is 2 SDs just below the mean.
Now, from the scores given, list down those that are less than 39.4 or greater than 66.2.
29,72,71,38
Hence, there are 4 scores that are more than 1 standard deviation away from the mean.
Compute for the final percentage.
50%-95%2
=50%-47.5%
=2.5%
The percentage of the tubs that weigh less than the labeled weight is 2.5%.
Simply get 2.5% of all the tubs surveyed.
2.5100=0.025
4000×0.025=100
Hence, 100 of the tubs weighed less than 1000g.
100
Question 3 of 4
3. Question
There are packets of sugar each labelled as 2kg. When the weights of 500 of these packets were checked, they were found to be normally distributed with a mean of 2.025kg and a standard deviation of 0.025kg. What percentage of these packets weigh less than the labelled weight?
First, complete the labels of the bell curve by using the mean and standard deviation.
For example, start with the mean, 2.025kg. Then add and subtract 0.025kg to get the values 1 standard deviation above and below the mean.
Keep adding and subtracting the standard deviation until the labels are completed.
In the curve, this means we are looking for the percentage from 2.000 to the left.
All the data below the mean (2.025) is 50%.
Knowing that 68% of the data lies 1 SD below and above the mean, we can say that the data between 2.000 and 2.025 is 34% because it is 1 SD just below the mean.
Compute for the final percentage.
50%-34%=16%
The percentage of the packets that weigh less than the labelled weight is 16%.
16%
Question 4 of 4
4. Question
There are packets of sugar each labelled as 2kg. When the weights of 500 of these packets were checked, they were found to be normally distributed with a mean of 2.025kg and a standard deviation of 0.025kg. The packaging machine is reset so that the average weight now is 2.050. What percentage is now less than the labelled weight?
First, complete the labels of the bell curve by using the mean and standard deviation.
For example, start with the mean, 2.050kg. Then add and subtract 0.025kg to get the values 1 standard deviation above and below the mean.
Keep adding and subtracting the standard deviation until the labels are completed.
We are asked about the percentage of packets that weigh less than the labelled weight, which is 2kg.
In the curve, this means we are looking for the percentage from 2.000 to the left.
All the data below the mean (2.050) is 50%.
Knowing that 95% of the data lies 2 SD below and above the mean, we can say that the data between 2.000 and 2.050 is 47.5% because it is 2 SD just below the mean.
Compute for the final percentage.
50%-47.5%=2.5%
The percentage of the packets that weigh less than the labelled weight is 2.5%, now that the machine is reset.