Blood samples are usually stored in plates of 16 wells 36 we

Blood samples are usually stored in plates of 16 wells, 36 wells, or 100 wells (e.g., a 16-well plate contains 16 blood samples). These samples are genotyped (a process of translating a blood sample into DNA sequence data) in plates. The heterozygosity of a blood sample is a measurement that is used to determine whether the sample is contaminated or failed to genotype. An unusually large or small average heterozygosity of the blood samples in a plate is often indicative of genotyping error or blood sample contamination. When this happens, further inspection on the entire plate is required.

The heterozygosity of a typical (successfully genotyped) blood sample follows a distribution with the following characteristics (percentile abbreviated as pctl):

1st pctl

5th pctl

25th pctl

50th pctl

Mean

75th pctl

95th pctl

99th pctl

SD

0.26

0.30

0.34

0.35

0.35

0.36

0.40

0.44

0.03

A blood sample is considered failed to genotype if it has a heterozygosity of at least 3 standard deviations away from the mean. A Co-op student was practising the genotyping procedure. The student randomly selected 500 blood samples from a pool of blood samples that were confirmed to be clean. Assume that there is a 500-well plate to store the 500 blood samples. Upon genotyping, he calculated the heterozygosity for each blood sample. The student found that 16 of the 500 samples were flagged as failed to genotype, and he was afraid that he did not learn the procedure right. Is the number of failures in the sample unusually high, low, or neither? Justify your answer using probability and make sure to state all assumptions.

Solution

16 / 500 = 0.032

we have this proportion and as you can see the proportion is very low

if you compare that value with the table of percentile you will find our number of failures in the sample unusually high because that value is lower than the percentile 1

that means that there is very small