Question

Suppose 140 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of theâ balance, not all the readings are equal. The results are found to closely approximate a normalâ curve, with mean 82 g and standard deviation 3 g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between 79 g and 85 g

Answer 1

Using the Empirical Rule, it is found that 95 students reported readings between 79 g and 85 g.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

• Approximately 68% of the measures are within 1 standard deviation of the mean.

• Approximately 95% of the measures are within 2 standard deviations of  the mean.

• Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, considering that the mean is of 82g and the standard deviation is of 3g, readings between 79g and 85g are within one standard deviation of the mean, hence it will compreend 68% of the 140 readings, so the number of students is given by:

0.68 x 140 = 95.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145