Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U( b. Suppose that 38 people are surveyed. What is the distribution of æ for this sample? a - N( c. What is the probability that the average birth month of the 38 people will be more than 4.8?

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**Statistical Analysis of Birth Month Distribution**

Treat the number of months \(X\) after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible.

**a. Distribution of \(X\):**  
What is the distribution of \(X\)?  
\[X \sim U(\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_)\]

**b. Distribution for a Sample of 38 People:**  
Suppose that 38 people are surveyed. What is the distribution of \(\bar{x}\) for this sample?  
\[\bar{x} \sim N(\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_)\]

**c. Probability Calculation:**  
What is the probability that the average birth month of the 38 people will be more than 4.8?  
\[\_\_\_\_\_\_\_\_\]
Transcribed Image Text:**Statistical Analysis of Birth Month Distribution** Treat the number of months \(X\) after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible. **a. Distribution of \(X\):** What is the distribution of \(X\)? \[X \sim U(\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_)\] **b. Distribution for a Sample of 38 People:** Suppose that 38 people are surveyed. What is the distribution of \(\bar{x}\) for this sample? \[\bar{x} \sim N(\_\_\_\_\_\_\_\_, \_\_\_\_\_\_\_\_)\] **c. Probability Calculation:** What is the probability that the average birth month of the 38 people will be more than 4.8? \[\_\_\_\_\_\_\_\_\]
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