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The weights of bags of baby carrots are normally distributed, with a mean of 32 ounces and a standard deviation of 0.32 ounce. Bags in the upper 4.5% are too heavy and must be repackaged. What is the most a bag of baby carrots can weigh and not need to be repackaged?

Respuesta :

Answer:

    [tex]x= 32.544[/tex]

Explanation:

given,

mean weight of bag (μ) = 32

standard deviation (σ) = 0.32

percentage of bag heavier = 4.5%

weight of the bag less than 4.5 % = 100 - 4.5

                                                        = 95.5%

we have to determine the z- value according to 95.5% or 0.955

using z-table

     z-value = 1.70

now, using formula

       [tex]Z = \dfrac{x-\mu}{\sigma}[/tex]

       [tex]1.70 = \dfrac{x-32}{0.32}[/tex]

       [tex]x-32 = 1.70\times {0.32}[/tex]

      [tex]x= 32.544[/tex]

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