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 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 between 87 g and 89 g.The number of students reporting readings between 87 g and 89 g is:________

Answer 1

The number of students reporting readings between 87 g and 89 g is 61

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 88g

Standard deviation = 1g

Percentage of students reporting readings between 87 g and 89 g

87 = 88-1

So 87 is one standard deviation below the mean.

89 = 88+1

So 89 is one standard deviation above the mean.

By the Empirical Rule, 68% of students are reporting readings between 87 g and 89 g.

Out of 90 students:

0.68*90 = 61.2

Rounding to the nearest whole number:

The number of students reporting readings between 87 g and 89 g is 61