Rice - packaging line

An automatic machine weighs rice into packages on a packaging line. Suppose that the mass of rice in a package is a random variable which has a normal probability distribution with mean value (Greek letter Mu) = 500 g and standard deviation (Greek letter Sigma) =5 g.
a) What is the probability that a randomly selected package will contain less than 495 g of rice?
b) Determine the mass that only 10% of the heaviest packages exceed.

Final Answer:

p =  0.1587
m₂ =  506.407 g

Step-by-step explanation:

$$\begin{gathered} \mu =500\text{g} \\ \sigma =5\text{g} \\ p=N(x<495g,\mu ,\sigma ) \\ p=0.1587 \end{gathered}$$

Use the normal distribution table.

$m_2=506.407=506.407\text{g}$

Try another example