Question

The manufacturers of m&m's claim that 20% of the milk chocolate m&m candies are orange. find the mean and standard deviation of the sampling distribution of the sample proportion of orange m&m's for samples of size 100. use two decimal places.

Answer 1

The mean of a sampling distribution of a sample with proportion, p and sample size, n is given by $\mu=np$.

The standard deviation of a sampling distribution of a sample with proportion, p and sample size, n is given by $\sigma= \sqrt{np(1-p)}$

Given that the manufacturers of m&m's claim that 20% of the milk chocolate m&m candies are orange. The proportion is p = 0.2

The mean of the sampling distribution of the sample proportion of orange m&m's for samples of size 100 is given by $\mu=100(0.2)=20$

The standard deviation of the sampling distribution of the sample proportion of orange m&m's for samples of size 100 is given by $\sigma= \sqrt{100(0.2)(1-0.2)} = \sqrt{16} =4$