The weights of bags of baby carrots are normally​ distributed, with a mean of 29 ounces and a standard deviation of 0.34 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?A bag of baby carrots can weigh at most______  ounces without needing to be repackaged.(Round to two decimal places as​ needed.)

Question
Asked Mar 5, 2019

The weights of bags of baby carrots are normally distributed, with a mean of 29 ounces and a standard deviation of 0.34 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?

A bag of baby carrots can weigh at most______  ounces without needing to be repackaged.

(Round to two decimal places as needed.)

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Expert Answer

Step 1

The weights of bags of baby carrots are normally distributed with mean 29 ounces and a standard deviation of 0.34 ounces. The repackaged bags are in the upper 4.5% (=0.045). Thus, the bag below 4.5% has not to be repackaged. This represents the area under the normal curve to the left of 0.955 (=1–0.045).

That is, to find how much a bag of baby carrots can weigh without needing to be repackaged is the x-value corresponding to the probability 0.955 is obtained.

Software Procedure:

Step by step procedure to find the x-value by using MINITAB software is as follows:

  • Choose Graph > Probability Distribution Plot > View Probability > OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Enter Mean as 29 and Standard deviation as 34.
  • Click the Shaded Area
  • Choose probability and Left Tail for the region of the curve to shade.
  • Enter the probability as 955.
  • Click OK.

Output using MINITAB software is as follows:

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Step 2

Thus, a bag of baby carrots can weigh at most 29.58 ounc...

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