Question

The population mean weight of a candy is 10 grams with a standard deviation of 2 grams. A sample of 100 candies is taken. What is the probability that the sample mean is at least 10.6 grams?

Answer 1

Let the original distribution function be F, then we need to perform:

$S=\sum\limits_{i=1}^n F(x_i)\geq1060$

From the Central limit theorem, the sum function will also be a normal distribution with a mathematical expectation of 1000 and a standard deviation of 200. Then apply the formula:

$P(S>10600)=Ф(\infty)-Ф(\frac{1060-1000}{200})=\\=0.5-0.1179=0,3821$

Where Ф is the Laplace function, the values are taken from the table