Question

Suppose 130 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

82g and standard deviation

1g. 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 85g.

Answer 1

Solution:

Given: 130 geology students measure the mass of an ore sample.

Thus n = 130

The results are found to closely approximate a normal​ curve, with mean 82g and standard deviation 1g.

Thus and

We have to use the empirical rule   to estimate the number of students reporting readings between 79 g and 85 g.

First find percent of data between 79 g and 85 g.

According to Empirical rule:

1) 68% of the data falls within 1 standard deviation from mean

2) 95% of the data falls within 2 standard deviation from mean

3) 99.7% of the data falls within 3 standard deviation from mean

Thus find k = number of standard deviation for given limits.

Lower limit = 79

and

Upper Limit = 85

Thus 79 and 85 are 3 standard deviations from the mean 82.

Thus using:

99.7% of the data falls within 3 standard deviation from mean

That is : 99.7% of the data is between 79 g and 85 g.

Now multiply this percent value by n = number of students

Thus:

the number of students reporting readings between 79 g and 85 g = 99.7% X 130

the number of students reporting readings between 79 g and 85 g = 0.997 X 130

the number of students reporting readings between 79 g and 85 g = 129.61

the number of students reporting readings between 79 g and 85 g = 130