Question

# We have a data set (n=100) with hormone concentrations and the frequency of each value. Assuming normal (continuous) distributions, We need to determine the parameters of the continuous probability distribution functions.

Data distributions
We have a data set (n=100) with hormone concentrations and the frequency of each value. Assuming normal (continuous) distributions, We need to determine the parameters of the continuous probability distribution functions.

2020-11-27
Step1
Let us suppose $$\displaystyle{X}_{{1}},{X}_{{2}},\ldots.,{X}_{{100}}$$ are samples from normal distribution
with mean $$\displaystyle\mu{\quad\text{and}\quad}{v}{a}{r}{i}{a}{n}{c}{e}\sigma^{{2}}$$
Hence, $$\displaystyle{X}_{{i}}\sim{N}{\left(\mu,\sigma^{{2}}\right)}$$
Here note that $$\displaystyle\mu{\quad\text{and}\quad}\sigma^{{2}}$$ are the parameters of the probability distribution
Now, You have calculated mean, Variance, and standard deviation of the samples.
Sample mean,$$\displaystyle\overline{{X}}=\frac{{1}}{{100}}\sum_{{i}}{X}_{{i}}$$,
sample variance , $$\displaystyle{S}^{{2}}=\frac{{1}}{{{100}-{1}}}{\sum_{{{i}={1}}}^{{100}}}{\left({X}_{{i}}-\overline{{x}}\right)}^{{2}}{N}{o}{w},{E}{\left(\overline{{x}}\right)}=\frac{{1}}{{100}}$$
$$\displaystyle\sum_{{i}}{\left({X}_{{i}}\right)}=\frac{{1}}{{100}}\times{100}\times\mu=\mu$$
and it can be shown $$\displaystyle{E}{\left({S}^{{2}}\right)}=\sigma^{{2}}$$
Step 2
Hence, the sample mean and sample variance are the estimates of the population parameter $$\displaystyle\mu{\quad\text{and}\quad}\sigma^{{2}}$$
The parameters of the probability distribution will be sample mean that you have calculated and sample variance that you have calculated.