The average American man consumes 9.5 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that this American man consumes between 9.2 and 10.1 grams of sodium per day. c. The middle 20% of American men consume between what two weights of sodium? Low: High:

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### Understanding Sodium Consumption in American Men

The average American man consumes 9.5 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let \( X \) represent the amount of sodium consumed. Please round all numeric answers to 4 decimal places where possible.

#### a. Distribution of \( X \)

\[ X \sim N(\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_) \]

- Fill in the mean and standard deviation values.

#### b. Probability Calculation

Find the probability that this American man consumes between 9.2 and 10.1 grams of sodium per day.

\[ P(9.2 \leq X \leq 10.1) = \_\_\_\_\_\_\_\_ \]

#### c. Middle 20% of Sodium Consumption

Determine the weights of sodium that correspond to the middle 20% of consumption among American men.

- **Low:** \[\_\_\_\_\_\_\_\_\]
- **High:** \[\_\_\_\_\_\_\_\_\]

These calculations are essential in understanding the distribution and consumption patterns of sodium among American men, which has implications for dietary guidelines and health initiatives.
Transcribed Image Text:### Understanding Sodium Consumption in American Men The average American man consumes 9.5 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let \( X \) represent the amount of sodium consumed. Please round all numeric answers to 4 decimal places where possible. #### a. Distribution of \( X \) \[ X \sim N(\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_) \] - Fill in the mean and standard deviation values. #### b. Probability Calculation Find the probability that this American man consumes between 9.2 and 10.1 grams of sodium per day. \[ P(9.2 \leq X \leq 10.1) = \_\_\_\_\_\_\_\_ \] #### c. Middle 20% of Sodium Consumption Determine the weights of sodium that correspond to the middle 20% of consumption among American men. - **Low:** \[\_\_\_\_\_\_\_\_\] - **High:** \[\_\_\_\_\_\_\_\_\] These calculations are essential in understanding the distribution and consumption patterns of sodium among American men, which has implications for dietary guidelines and health initiatives.
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