Question

The flu shot for a flu season is created from four strains of the flu virus, named Strain A, B, C and D, respectively. Medical researchers use the following data to determine the effectiveness of the vaccine over the flu season. Table $1$ shows the effectiveness of the vaccine against each of these strains individually. The graph shows the prevalence of each of these strains during each month of the flu season, represented as a percentage of the overall cases of flu that month. For the strain against which the flu shot was the most effective, approximately how effective was the shot overall when that strain was least prevalent?

Strain	Effectiveness
A	$35\%$
B	$13\%$
C	$76\%$
D	$68\%$

• A. $13\%$
• B. $27\%$
• C. $30\%$
• D. $48\%$

Answer 1

The correct option is D $48\%$

The flu shot is most effective against Strain C, which is least prevalent in March.

To determine the overall efficacy of the flu shot at this time, multiply the prevalence of each strain of flu by the efficiency of the flu shot against that strain and then add those products to get a weighted average of the efficacy of the shot:

$(0.23\times 0.35)+(0.25\times 0.13)+(0.13\times 0.76)+(0.39\times 0.68)$

$=0.0805+0.0325+0.0988+0.2652$

$=0.477$.

Then $\%$ of this =$0.477\times 100=47.7$ which is closest to (D).