Question

A manufacturing process outputs parts having a normal distribution with a mean of 30 cm and standard deviation of 2 cm. From a production sample of 80 parts, what proportion of the sample can be expected to fall between 28 and 32 cm

Answer 1

68% of the sample can be expected to fall between 28 and 32 cm

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 = 30

Standard deviation = 2

What proportion of the sample can be expected to fall between 28 and 32 cm

28 = 30 - 2

28 is one standard deviation below the mean

32 = 30 + 2

32 is one standard deviation above the mean.

By the Empirical Rule, 68% of the sample can be expected to fall between 28 and 32 cm