Caffeinated Beverages and Diabetes. The objective of the article, “Caffeinated a
ID: 3042997 • Letter: C
Question
Caffeinated Beverages and Diabetes. The objective of the article, “Caffeinated and Caffeine-free Beverages and Risk of Type 2 Diabetes” (American Journal of Clinical Nutrition, Vol. 97, No. 1, pp. 155–166) by S. Bhupathiraju et al., was to examine the association between caffeinated beverages and type 2 diabetes risk. The mean and standard deviation of the body mass index (BMI) for a sample of 10,215 women who drink at least one caffeinated carbonated beverage a day are 25.7 and 5.3, respectively.
a.At least how many women in the sample have a BMI of between 15.1 and 36.3?
b.Fill in the blanks: At least 89% of the women in the sample have BMIs between ______ and ______.
Explanation / Answer
for 15.1 and 36.3 are 2 std deviation away from mean ; and from Chebychev;s at least 75% values fall with in 2 std deviation from mean.
hence number of women in the sample have a BMI of between 15.1 and 36.3 =10215*0.75 =7661.25
b)
for 89% values fall with in 3 std deviation away from mean
hence corresponding values =25.7-/+ 3*5.3 =9.8 to 41.6
At least 89% of the women in the sample have BMIs between 9.8 and 41.6.