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The antibody response that a potential vaccine induces, measured by an "antibody score", is one approach...

The antibody response that a potential vaccine induces, measured by an "antibody score", is one approach for determining the vaccine's effectiveness. Any potential vaccine with an antibody score greater than 139 is considered to be effective. For any given potential vaccine for a new virus, suppose the antibody score is normally distributed with unknown mean \mu and variance 169. Further, for this new virus, only 23% of potential vaccines are known to be effective. Find the value of \mu, the mean antibody score for potential vaccines for this new virus.

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