Question

A study of the nutritional value of a certain kind of bread shows that on the average one slice contains 0.260 milligram of thiamine (vitamin B1) with a standard deviation of 0.005 milligram. According to Chebyshev's theorem, between what values must the thiamine content be of

(a) at least 35/36 of all slices of this bread; (0.230 and 0.290)

(b) at least 80/81 of all slices of this bread? (0.215 and 0.305)

Answer 1

Chebychev's Theorem: 0) |Pl 0.260-0.005k X 0.260 + 0.005k)2 1- 135 -k2-36 ( a ) Given : 1 From(1). Lowe, value-0.260-(0.005 x 6)= 0.230 Upper value 0.260 (0.005x6)-0.290 b) Given: 1---- 1 80 k2 81 From(1 Lower value 0.260 (0.005 x9)-0.215 Upper value 0.260(0.005x9) 0.305