Question

Suppose 170 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 83 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 74g and 92g

Answer 1

Using the empirical rule, about 99.7% of the 170 geology students' measurements of the ore sample are expected to fall within three standard deviations (74g to 92g) of the mean (83g).

Step-by-step explanation:

The student has asked to estimate the number of geology students reporting ore sample readings between 74g and 92g, given that the mass measurements approximate a normal curve with a mean of 83g and a standard deviation of 3g. To solve this, we can use the empirical rule which states that approximately 68% of data within a normal distribution falls within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations. Since 74g to 92g encompasses three standard deviations from the mean (74g = 83g - 3(3g), 92g = 83g + 3(3g)), we would expect about 99.7% of the measurements to fall within this range.

To estimate the number of students, we take 99.7% of the total number of students, which is 170. So, 0.997 x 170 ≈ 169.46. Therefore, we can estimate that approximately 169 students reported readings between 74g and 92g.