It is important to note the type of distribution of such sampling.
To choose a candy, it can either be 'orange' or 'not orange'.
The sample size of 100 is large enough. Hence, the sampling describes Binomial Distribution.
The mean and standard deviation of a Binomial Distribution, respectively is given as:
[tex]\begin{gathered} \mu=np \\ \sigma=\sqrt[]{np(1-p)}_{} \end{gathered}[/tex]Where,
0. n= number of trials or samples
,1. p=probability of success (orange candies)
As given in the sample, n=100, p=10% or 0.1
Substitute into the formula given:
[tex]\mu=100\times0.1=10[/tex][tex]\sigma=\sqrt[]{100\times0.1(1-0.1)}=\sqrt[]{100\times0.1\times0.9}=\sqrt[]{9}=3[/tex]Hence, the mean is 10 and the standard deviation is 3.
