# Statistics

When red blood cells are counted using a certain electronic counter, the standard deviation (SD)
of repeated counts of the same blood specimen is about .8% of the true value, and the distribution
of repeated counts is approximately normal. For example, this means that if the true value is
5,000,000 cells/mm3, then the SD is 40,000.
(a) If the true value of the red blood count for a certain specimen is 5,000,000 cells/mm3, what
is the probability that the counter would give a reading between 4,900,000 and 5,100,000?
(b) of the true value of the red blood count for a certain specimen is ì, what is the probability
that the counter would give a reading between .98ì and 1.02ì?
(c) A hospital lab performs counts of many specimens every day. For what percentage of these
specimens does the reported blood count differ from the correct value by 2% or more?
I need help with part C.
part A & B I get it
this Q is from the book and the final answer of C is 1.24% as in the book but I need to find how I reach to this answer
thanks

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1. You subtract 1 from the answer you got in b). You would end up with 0.0124 or 1.24%. This is because the range for b) differs from the mean by 2% or less of the mean.
Another way:
since you are finding 2% or more away from the corrected value, it would be easier if you put the mean as 100, therefore 2%+ away from 100 is 98 and below and 102 and above.
Now you can find the probabilities P(x<98) and P(x>102). Add them up and you get your answer.

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