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May 2nd, 2017, 05:18 AM  #1 
Newbie Joined: Apr 2017 From: London Posts: 4 Thanks: 0  Stuck on probability distribution of a normal distribution problem https://gyazo.com/921c2e7fd4ace575e11c5fc0afcedee0 Any ideas on how to approach part iii? Thanks alot 
May 2nd, 2017, 10:51 AM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,237 Thanks: 637 
you should know that if two normal random variables $X \sim N(\mu_x, \sigma_x),~Y \sim N(\mu_y, \sigma_y)$ then $X + Y \sim N\left(\mu_x+\mu_y,\sqrt{\sigma_x^2 + \sigma_y^2}\right)$ and $c X \sim N(c \mu_x, c \sigma_x)$ so the mean of $N$ identically distributed normal random variables, $X$, will be distributed as $\bar{X} \sim N\left(\mu_x, \dfrac{\sigma_x}{\sqrt{N}}\right)$ this should let you complete part 3 

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distribution, normal, probability, problem, stuck 
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