Thread: Normal distribution

1. Normal distribution

Statistics help? X is distributed normally, P(x>=59.1) =0.0218 and P(x>=29.2)=0.9345 Find the mean and standard deviation of the distribution, correct to 3 significant figures.

2. Re: Normal distribution

If you are expected to do this kind of problem then you should know that, given a normal distribution with mean $\displaystyle \mu$ and standard deviation $\displaystyle \sigma$, variable x corresponds to a "standard normal distribution" $\displaystyle z= \frac{x- \mu}{\sigma}$. Here, you need to look up, in a table of the standard normal distribution, $\displaystyle z_0$ corresponding to $\displaystyle P(z\ge z_0)= 0.0218$ and $\displaystyle z_1$ such that $\displaystyle P(z\ge z_1)= 0.9345$. Then, using those values for $\displaystyle z_0$ and $\displaystyle z_1$, solve the two equations $\displaystyle z_0= \frac{59.1- \mu}{\sigma}$ and $\displaystyle z_1= \frac{29.2- \mu}{\sigma}$ for $\displaystyle \mu$ and $\displaystyle \sigma$.