b. If 9 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.
b. If 9 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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I need the solution for B please?

Transcribed Image Text:### Understanding Weight Gain Among Male College Freshmen
This section analyzes the weight gain of male college students during their freshman year, assuming the data follows a normal distribution. Here are some key insights based on the statistics provided:
#### Statistical Overview:
- **Mean (μ):** 1.4 kg
- **Standard Deviation (σ):** 5.1 kg
#### Probability Calculations:
**a. Single Student Weight Gain Probability**
- **Scenario:** For one randomly selected male student, calculate the probability that he gains between 0 kg and 3 kg in his freshman year.
- **Result:** The probability is **0.2313**. (The calculation is rounded to four decimal places for precision.)
**b. Group Average Weight Gain Probability**
- **Scenario:** For a group of 9 randomly selected male students, determine the probability that their average weight gain is between 0 kg and 3 kg during their freshman year.
Complete these calculations using appropriate statistical methods to understand trends in weight gain among male college freshmen better.
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