Question

Suppose 110 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the​ balance, not all the readings are equal. The results are found to closely approximate a normal​ curve, with mean 82 g and standard deviation 2 g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between 76 g and 88 g.

Answer 1

Solution:

We are given:

To find the number of students reporting readings between 76 g and 88 g, we have to first find the area between 76 g and 88 g

Using the z-score formula, we have:

  

The empirical rule of the normal distribution says about 99.7% of the data falls within three standard deviations of the mean.

Therefore, the number of students reporting readings between 76 g and 88 g is: