Questions: The weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g. a. For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what is the area under the curve? b. What is the value of the median? a. For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what is the area under the curve? (Type an integer or a decimal. Do not round.) b. What is the value of the median? g (Round to four decimal places as needed.)

The weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g. a. For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what is the area under the curve? b. What is the value of the median? a. For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what is the area under the curve? (Type an integer or a decimal. Do not round.) b. What is the value of the median? g (Round to four decimal places as needed.)
Transcript text: The weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g. a. For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what is the area under the curve? b. What is the value of the median? a. For the bell-shaped graph of the normal distribution of weights of Hershey Kisses, what is the area under the curve? (Type an integer or a decimal. Do not round.) b. What is the value of the median? $g$ (Round to four decimal places as needed.)
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Solution

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Solution Steps

Step 1: Area Under the Curve

For a normal distribution, the area under the curve is always equal to 1. This represents the total probability of all possible outcomes.

\[ \text{Area under the curve} = 1.0 \]

Step 2: Value of the Median

In a normal distribution, the mean (\( \mu \)) is equal to the median. Given that the mean weight of the Hershey Kisses is \( 4.5338 \, g \), we can conclude that:

\[ \text{Median} = \mu = 4.5338 \, g \]

Final Answer

\[ \text{Area under the curve} = \boxed{1.0} \] \[ \text{Median} = \boxed{4.5338 \, g} \]

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