
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 13th, 2017, 10:35 AM  #1 
Senior Member Joined: Jan 2013 From: Italy Posts: 154 Thanks: 7  Find standard deviation given normal probability
I have $X \sim N(0,\sigma^2), Y \sim N(1,4) \mbox{ independent}, \\ Z = XY$ find $\sigma$ such that $P(Z \le 7) = 0.84134$ what I have done is : $XY \sim N(0(1), \sigma^2+4) = (1, \sigma^2+4)$ $\begin{array}{lcl}P(Z \le 7) & = & P( \frac{Z 1}{\sqrt{\sigma^2+4}} \le \frac{71}{\sqrt{\sigma^2+4}}) \\ & = & P(W \le \frac{6}{\sqrt{\sigma^2+4}}) &= & 0.84137 \end{array}$ $W \sim N(0,1) \\ 0.84137 = \phi(1) \mbox{ therefore }$ $\begin{array}{lcl}\frac{6}{\sqrt{\sigma^2+4}} & = & 1 \\ \frac{36}{\sigma^2+4} & = & 1 \\ \frac{36(\sigma^2+4)}{\sigma^2+4} & = & \sigma^2+4 \\ 36 & = & \sigma^2 + 4 \\ \sigma^2 &= & 32 \\ \sigma & = & \sqrt{32} \end{array}$ please, can you tell me if it's correct? Thanks! 
November 14th, 2017, 12:51 AM  #2 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 Thanks: 60 Math Focus: सामान्य गणित 
seems correct


Tags 
deviation, find, normal, normal distribution, probability, standard, standard deviation 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How do I find the Mean and Standard Deviation for this probability  Ore0Kidd  Probability and Statistics  1  March 6th, 2016 10:23 PM 
Normal Distribution: Calculating Mean and Standard Deviation  wahhdoe  Probability and Statistics  6  February 10th, 2016 01:37 AM 
Probability Distribution and Standard Deviation  EvanJ  Advanced Statistics  4  December 23rd, 2013 08:35 AM 
Probability and standard deviation  ragas88  Advanced Statistics  1  July 27th, 2013 08:55 AM 
find expected value, standard deviation, and probability  jd254  Algebra  0  May 7th, 2009 12:46 AM 