a drug test is 97% accurate. 2000 people take the test. 1975 of the people do not use drugs, while the other 25 are drug users. How many non-drug users will pass the drug test?
1975 are non-users ... 97% will be correctly identified
.97 * 1975 = ?
To find out how many non-drug users will pass the drug test, we need to first determine how many people will be accurately identified as non-drug users by the test.
Given that the test is 97% accurate, it means that it correctly identifies 97% of the non-drug users and 97% of the drug users.
First, we calculate how many non-drug users will be correctly identified by the test:
97% of 1975 (non-drug users) = 0.97 * 1975
= 1914.75 (rounded to the nearest whole number)
So, about 1915 non-drug users will be correctly identified as non-drug users.
Next, we calculate how many drug users will be incorrectly identified by the test:
3% of 25 (drug users) = 0.03 * 25
= 0.75 (rounded to the nearest whole number)
So, about 1 drug user will be incorrectly identified as a non-drug user.
Now, we subtract the number of incorrectly identified drug users from the total number of non-drug users to get the number of non-drug users who will pass the drug test:
Number of non-drug users who will pass = 1975 - 1
= 1974
Therefore, approximately 1974 non-drug users will pass the drug test.