Suppose that from given statistics, it is known that meningitis causes stiff…
2015
Suppose that from given statistics, it is known that meningitis causes stiff neck 50% of the time, that the proportion of persons having meningitis is \(\frac{1}{50000}\), and that the proportion od people having stiff neck is \(\frac{1}{20}\). Then the percentage of people who had meningtis and complain about stiff neck is:
- A.
0.01%
- B.
0.02%
- C.
0.04%
- D.
0.05%
Attempted by 33 students.
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Correct answer: B
Key idea: Find the joint probability by multiplying the prevalence of meningitis by the probability of stiff neck given meningitis.
Prevalence of meningitis = 1/50000 = 0.00002.
Probability of stiff neck given meningitis = 50% = 0.5.
Joint probability = 0.00002 × 0.5 = 0.00001.
Convert to a percentage: 0.00001 × 100 = 0.001%.
Therefore the correct percentage of people who had meningitis and complain of stiff neck is 0.001%.
None of the provided answer choices (0.01%, 0.02%, 0.04%, 0.05%) equal 0.001%; each is considerably larger (for example, 0.01% is 10 times larger).