Answer:
The value is [tex]x = 5.0744 \ ounce[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 5 \ ounce[/tex]
The standard deviation is [tex]\sigma = 0.3 \ ounce[/tex]
Generally the minimum weight of the heaviest 9.8% is mathematically represented as
[tex]P(X > x ) =P( \frac{X - \mu}{\sigma } > \frac{x -5}{0.3} ) = 0.098[/tex]
=> [tex] P(X > x ) =P( Z > \frac{x -5}{0.3} ) = 0.098[/tex]
From the normal distribution table the z-score for 0.098 is
[tex]z =0.248[/tex]
So
[tex]\frac{x -5}{0.3} = 0.248[/tex]
=> [tex]x = 5.0744 \ ounce[/tex]
