Question

Suppose 180 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 88 g and standard deviation 1 g. use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings more than 88 g

Answer 1

Given the total number of students are 180, the mean of data is 88g, and standard deviation is 1g.

A normal curve is a bell-shaped curve with symmetry about the mean and it spreads uniformly on both sides (left side and right side) of the mean.

The empirical rule is also called "68-95-99.7" rule. It says that :-

A) 68% of the data values fall between 1 standard deviation about mean (34% on left side and 34% on right side),

B) 95% of the data values fall between 2 standard deviations about mean (47.5% on left side and 47.5% on right side), and

C) 99.7% of the data values fall between 3 standard deviations about mean (49.85% on left side and 49.85% on right side).

According to distribution of normal curve and "68-95-99.7" empirical rule, we can say 49.85% of data values are above the mean within 3 standard deviations.

So it means 49.85% of total students report readings more than 88g.

Number of students reporting readings more than 88g = 49.85% of 180 = 0.4985 × 180 = 89.73

Hence, approximately 89 students report readings more than mean value.