Question

2. At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

Answer 1

$P(0.99<\bar X<1.01)=P(\frac{0.99-1}{\frac{0.1}{\sqrt{12}}}<Z<\frac{1.01-1}{\frac{0.1}{\sqrt{12}}})=$

$=P(-0.35<Z<0.35)=P(Z<0.35)-P(Z<-0.35)=0.2737.$