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 2 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 87 g.
the number of students reporting readings between 79 g and 87 g is .
(round to the nearest whole number as needed.)

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 83$ (mean), $\sigma = 2$ (standard deviation).
For $x = 79$, $z_1=\frac{79 - 83}{2}=\frac{-4}{2}=-2$.
For $x = 87$, $z_2=\frac{87 - 83}{2}=\frac{4}{2}=2$.

Step2: Use the empirical rule

The empirical rule for a normal distribution states that approximately 95% of the data lies within $z=- 2$ and $z = 2$.

Step3: Calculate the number of students

The total number of students is $n = 170$.
The number of students with readings between 79 g and 87 g is $0.95\times170 = 161.5\approx162$.

Answer:

162