Question

suppose 90 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 result are found to closely approximate a normal curve with mean 88 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 97 g round to the nearest whole number as needed

Answer 1

The empirical rule states that

1) About 68% of the values of x lies between one standard deviation below and above the mean.

2) About 95% of the values of x lies between two standard deviation below and above the mean.

3) About 99.7% of the values of x lies between three standard deviation below and above the mean.

Looking at the given scenario, let x represent the mass of an ore sample. Given that

mean = 88g

standard deviation = 3g

For a reading of 79g below the mean, 88 - 79 = 9g

9g = 3 standard deviations below the mean.

For a reading of 97g below the mean, 97 - 88 = 9g

9g = 3 standard deviations above the mean.

By applying the empirical rule, we can conclude that about 99.7% of the measured mass readings lie between 79g and 97g

Given that 90 students carried out measurements, the number of students reporting readings between 79 g and 97 g is

99.7/100 * 90 = 89.73

Rounding to the nearest whole number, it becomes 90 students