Question

The lifetime of a certain type of automatic machine is normally distributed with mean and standard deviation equals to 3.1 and 1.1 years repspectivelly, use the standard normal table to find P left parenthesis x less than 3.3 right parenthesis

Answer 1

$X\sim N(3.1, 1.1^2)$

$$P(X<3.3)=P(Z<\dfrac{3.3-\mu}{\sigma})$$

$$=P(Z<\dfrac{3.3-3.1}{1.1})\approx P(Z<0.181818)$$

$$\approx0.572137$$