Question

X: Vitamin B1 content of a slice of bread µ= 3 microgram and σ= 0.005 milligram

a) According to Chebyshev’s Theorem, what is the interval of vitamin B1 content that at least 8 out of 9 slices of bread satisfy?

b) Assume that X has a normal distribution, find the exact probability of observing the interval you find in part a). Compare and discuss the results.

Answer 1

Solution:

a) We know that:

Therefore, the interval of vitamin B1 content that at least 8 out of 9 slices of bread satisfy is:

(b) We are required to find:

Using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, about 99.7% of the data lies within three standard deviations of the mean value as per the normal distribution, while at least 89% of the data lies within three standard deviations of the mean value as per the Chebyshev's theorem.