A machine

A machine produces steel rods of normally distributed length, the mean length and the standard deviation being 50.0 cm and 0.5 cm, respectively. The rods do not conform to safety standards if they are either shorter than 49.1 cm or longer than 50.7 cm in length. Find the number of rods from a consignment of 5000 rods that do not conform to safety standards.

Correct answer:

x =  584

Step-by-step explanation:

$$\begin{gathered} m=50.0\text{cm} \\ \sigma =0.5\text{cm} \\ t=5000 \\ p\dots N(m,\sigma ) \\ {p}_1=49.1<l\vee l>50.7 \\ {p}_1=0.1167 \\ x=p_1\cdot t=0.1167\cdot 5000=584 \end{gathered}$$

Use the normal distribution table.

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