How can I simulate a normal distribution from means and 95% confidence limits? [duplicate]

Well, I have these values: $\mathrm{Mean}=5.77$; $95\%\mathrm{CL}=5.30-6.11$

How can I simulate a normal distribution using these parameters? I do not have standard deviations.

How can I obtain random values (for example, 1000 of them) that fit to these parameters? (like using the rnorm function when having Standard deviations except $95\%CLs$)

• Do you need exactly the given values or just reasonable approximations? Commented Feb 19, 2014 at 12:05
• Welcome to Cross Validated! You might want to explain the situation a little more to make sure the answers are helpful. As I understand it you don't know any parameters, but you have an estimate of one - the population mean. You also have a confidence interval for it. If you know how both were calculated from the sample you may be able to estimate the population standard deviation. Commented Feb 19, 2014 at 12:13
• I have some papers with data, and they are about dental eruption in modern humans. They only publish the average age for one of the tooth with its 95%CLs. For example, the molar in an African population erupts in average at 5.77 years with a 95%CL of 5.30-6.11. These values are given for every tooth and for different populations. So, what I'd like to do is to simulate, if possible, the normal distribution with those values (average and 95%CL) and to get a different number of values that may fit with those requisites. Commented Feb 19, 2014 at 15:26
• Closely related (with helpful information): stats.stackexchange.com/questions/22021 (computing standard errors from CIs), stats.stackexchange.com/questions/29594 (the binomial version of this question), stats.stackexchange.com/questions/18215 (examples of closely related calculations with CIs), stats.stackexchange.com/questions/65101 (the lognormal version of this question). For more, please search our site.
– whuber
Commented Feb 19, 2014 at 15:51
• I forgot to say that I want to do it using R-project software. Thanks for your answer whuber, but I have not find this task on this web using R. Thanks Commented Feb 19, 2014 at 16:45