EAR- Estimated Average Requirement
RDA- Recommended Dietary Allowance
Given, The EAR for Vitamin B12 is 2.0 microgram and RDA is 2.4 microgram.
Prevalence= No. of people affected by it/ Total number of population
Hence, No. of people consuming insufficient Vitamin B12 Would be all the elderly residents in the nursing home who consume less than 1.6 mcg, 1.6-1.7 mcg and more than or equal to 2.6 mcg of Vitamin B12; which would be 5, 20 and 5 respectively.
Total population of the elderly residents in the nursing home= 100
Prevalence of inadequate Vitamin B12 consumption= 5+20+5/100= 0.3= 30%
NOTE= as you've stated in the question above that 20+5+5/100= 45% is mathematically wrong. It would give you 0.3 which when converted in % form would become, 30%.
However, Your statement above has not included people who consume Vitamin B12 between 1.8-1.9 mcg, which falls below the EAR and hence, also inadequate.
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