Mars, Inc. claims that 20% of its M&M plain candies are orange. A sample of 100 such candies is randomly selected. Find the mean and standard deviation for the number of orange candies in such groups of 100 .
A) $\mu = 20 , \sigma = 4.0$
B) $\mu = 20 , \sigma = .20$
C) $\mu = .020 , \sigma = .20$
D) $\mu = .20 , \sigma = 4.0$

Question

Mars, Inc. claims that  20%  of its M&M plain candies are orange. A sample of 100 such candies is randomly selected. Find the mean and standard deviation for the number of orange candies in such groups of 100 .
A) $\mu = 20 , \sigma = 4.0$
B) $\mu = 20 , \sigma = .20$
C) $\mu = .020 , \sigma = .20$
D) $\mu = .20 , \sigma = 4.0$

Quizplus · Accepted Answer

The mean ($\mu$) of orange candies in a sample of 100 is found using the formula $\mu = np$, where $n = 100$ (the sample size) and $p = 0.20$ (the probability of getting an orange candy). Thus, $\mu = 100 \times 0.20 = 20$. The standard deviation ($\sigma$) is found using the formula $\sigma = \sqrt{np(1-p)}$, which gives $\sigma = \sqrt{100 \times 0.20 \times (1-0.20)} = \sqrt{16} = 4.0$.

Mars, Inc Claims That 20% of Its M&M Plain