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.)

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:

Step 2

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

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