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 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 $X \sim N(0,\sigma^2), Y \sim N(-1,4) \mbox{ independent}, \\ Z = X-Y$ find $\sigma$ such that $P(Z \le 7) = 0.84134$ what I have done is : $X-Y \sim N(0-(-1), \sigma^2+4) = (1, \sigma^2+4)$ $\begin{array}{lcl}P(Z \le 7) & = & P( \frac{Z -1}{\sqrt{\sigma^2+4}} \le \frac{7-1}{\sqrt{\sigma^2+4}}) \\ & = & P(W \le \frac{6}{\sqrt{\sigma^2+4}}) &= & 0.84137 \end{array}$ $W \sim N(0,1) \\ 0.84137 = \phi(1) \mbox{ therefore }$ $\begin{array}{lcl}\frac{6}{\sqrt{\sigma^2+4}} & = & 1 \\ \frac{36}{\sigma^2+4} & = & 1 \\ \frac{36(\sigma^2+4)}{\sigma^2+4} & = & \sigma^2+4 \\ 36 & = & \sigma^2 + 4 \\ \sigma^2 &= & 32 \\ \sigma & = & \sqrt{32} \end{array}$ 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: 901 Thanks: 61 Math Focus: सामान्य गणित seems correct Tags deviation, find, normal, normal distribution, probability, standard, standard deviation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Ore0Kidd Probability and Statistics 1 March 6th, 2016 10:23 PM wahhdoe Probability and Statistics 6 February 10th, 2016 01:37 AM EvanJ Advanced Statistics 4 December 23rd, 2013 08:35 AM ragas88 Advanced Statistics 1 July 27th, 2013 08:55 AM jd254 Algebra 0 May 7th, 2009 12:46 AM

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