during the initial months of the covid-19 pandemic, resources for testing samples for the disease were scarce. what if specimens were pooled and several samples were tested at once? if the pool tested negative, then all of the individuals who submitted specimens in the sample are free from the disease. if the pool tested positive, then at least one of the specimens in the pool was positive, and all of the specimens in the pool would be tested individually. in the long run, does this procedure result in fewer tests?
assume that 5% of specimens that are tested for covid-19 yield positive results. (the actual rate was much higher when testing was not extensive, but overall, when testing is being done extensively, 5% is a reasonable estimate.)
suppose that 1 million people present themselves for testing and that specimens are pooled together in groups of size 5. what is the expected number of tests that would have to be performed?

one million specimens were pooled into groups of five specimens each, for a total of (\frac{1,000,000}{5} = 200,000) groups that were tested. the probability that a group of five specimens tests positive is 0.226219.
how many of the 200,000 groups that were tested would you expect to test positive? give your answer rounded up to the next highest whole number.
expected number of groups: (square) groups

Question

during the initial months of the covid-19 pandemic, resources for testing samples for the disease were scarce. what if specimens were pooled and several samples were tested at once? if the pool tested negative, then all of the individuals who submitted specimens in the sample are free from the disease. if the pool tested positive, then at least one of the specimens in the pool was positive, and all of the specimens in the pool would be tested individually. in the long run, does this procedure result in fewer tests?
assume that 5% of specimens that are tested for covid-19 yield positive results. (the actual rate was much higher when testing was not extensive, but overall, when testing is being done extensively, 5% is a reasonable estimate.)
suppose that 1 million people present themselves for testing and that specimens are pooled together in groups of size 5. what is the expected number of tests that would have to be performed?

one million specimens were pooled into groups of five specimens each, for a total of (\frac{1,000,000}{5} = 200,000) groups that were tested. the probability that a group of five specimens tests positive is 0.226219.
how many of the 200,000 groups that were tested would you expect to test positive? give your answer rounded up to the next highest whole number.
expected number of groups: (square) groups

Accepted Answer

# Explanation:
## Step1: Identify the number of groups
We know there are 1,000,000 specimens and they are pooled into groups of 5. So the number of groups is calculated as $\frac{1000000}{5} = 200000$ groups.

## Step2: Calculate the expected number of positive groups
The probability that a group of five specimens tests positive is given as 0.226219. To find the expected number of positive groups, we multiply the total number of groups by this probability. So we calculate $200000	imes0.226219$.

## Step3: Perform the multiplication and round up
First, calculate $200000	imes0.226219 = 45243.8$. Then, we need to round up to the next highest whole number. Since 45243.8 is not a whole number, the next highest whole number is 45244.

# Answer:
45244

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Question

Explanation:

Step1: Identify the number of groups

Step2: Calculate the expected number of positive groups

Step3: Perform the multiplication and round up

Answer: