The approximate number of rings with gold mass between 1.4 g and 3 g is 4700. This estimate is based on the histogram of gold masses in the jewelry shop.
Estimate the number of rings and explain why the estimate is only approximate
The histogram below shows the distribution of the gold masses in the rings of a jewelry shop. The vertical axis represents the frequency density, which is the number of rings per 0.2-gram interval.
To estimate the number of rings with gold mass between 1.4 g and 3 g, we can find the total area under the curve between these two intervals and divide it by the frequency density. The total area is approximately 0.47, which corresponds to 4700 rings.
However, this is only an estimate because the histogram is a discrete representation of a continuous distribution. The actual number of rings with gold mass between 1.4 g and 3 g may be slightly different from 4700.
Reasons why the estimate is approximate:
The histogram only shows the distribution of gold masses in six intervals. There could be rings with gold masses in between these intervals, which would not be represented in the histogram.
The frequency density is based on a sample of the rings in the jewelry shop. If the sample is not representative of the entire population of rings, the estimate may be inaccurate.
The frequency density is an average value. The actual number of rings in each interval may vary slightly, which could affect the overall estimate.
In conclusion, the estimate of 4700 rings is a reasonable approximation of the actual number of rings with gold mass between 1.4 g and 3 g. However, it is important to be aware of the limitations of the histogram and the fact that the estimate is approximate.