The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. (a) Find the z-score corresponding to 38 percent of fat calories, rounded to 3 decimal places. (b) Find the probability that the percent of fat calories a person consumes is more than 38. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (a), rounded to one decimal place).
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. (a) Find the z-score corresponding to 38 percent of fat calories, rounded to 3 decimal places. (b) Find the probability that the percent of fat calories a person consumes is more than 38. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x- axis is the z-score. Use your z-score from part (a), rounded to one decimal place).
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:**Educational Website Content on Fat Calorie Consumption in America**
The percentage of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let \( X \) represent the percent of fat calories.
**Tasks:**
**(a)** Find the z-score corresponding to 38 percent of fat calories, rounded to 3 decimal places.
- Input area for the z-score calculation.
**(b)** Find the probability that the percent of fat calories a person consumes is more than 38.
- Input area for the probability calculation.
**(c)** Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place).
- A dropdown menu reads "Shade: Left of a value," with an interactive feature to click and drag arrows to adjust values on the graph.
- **Graph Description:**
- A standard normal distribution curve is shown, with the x-axis labeled as the z-score, ranging from -4 to 4.
- The shaded blue area is to the left of the z-score value -1.5.
- This shading visually represents the probability associated with a z-score less than -1.5.
**(d)** Find the maximum number for the lower quarter of the percent of fat calories. Round your answer to 3 decimal places.
- Input area for calculation.
**(e)** Sketch the graph and write the probability statement.
- Textbox with editing options, including bold, italics, underline, and other formatting tools.
This content provides a detailed scenario for understanding the probabilities and z-scores associated with a normally distributed dataset, reflecting real-world applications in dietary analysis.
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