Question

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(0, 12) b. Suppose that 37 people are surveyed. What is the distribution of X̄ for this sample? X̄ ~ N(μ, σ^2) c. What is the probability that the average birth month of the 37 people will be less than 6.3?

Name: 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 xx 89394
Uploaded: 2023-04-04T05:20:02-08:00
Duration: 4 min 8 s
Channel: Sri K
Description: 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 xx 89394

          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(0, 12)
b. Suppose that 37 people are surveyed. What is the distribution of X̄ for this sample? X̄ ~ N(μ, σ^2)
c. What is the probability that the average birth month of the 37 people will be less than 6.3?

Added by Samantha W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

04/04/2023

Step 1

Since X is uniformly distributed from 0 to 12, we can write the distribution of X as: $$ X \sim U(0, 12) $$ b. Now, we want to find the distribution of the sample mean $\bar{X}$ for a sample of 37 people. According to the Central Limit Theorem, the distribution Show more…

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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(0, 12) b. Suppose that 37 people are surveyed. What is the distribution of X̄ for this sample? X̄ ~ N(μ, σ^2) c. What is the probability that the average birth month of the 37 people will be less than 6.3?