Question

bag of smokeless fuel are labeled as weighing 100kg but actual weights are normally distributed with a mean of 102kg and a standard deviation of 4kg.
What proportion of bag will weigh more than 106kg

Answer 1

Let $X=$ the weight of bag: $X\sim N(\mu, \sigma^2)$

$$Z={X-\mu\over \sigma}\sim N(0,1)$$

Given $\mu=102, \sigma=4$

$$P(X>106)=1-P(X\leq106)=1-P(Z\leq{106-102\over 4})=$$

$$=1-P(Z\leq1)\approx0.1587$$

$15.87\ \%$