Lengths 6

Lengths of 130 tubes are measured. The arithmetic mean is 17.27 cm, and the standard deviation is 1.2 cm. How many tubes do have a length:
a) between 16.5 cm and 18.1 cm
b) greater than 17 cm

Correct answer:

a =  64
b =  77

Step-by-step explanation:

$$\begin{gathered} m=17.27\text{cm} \\ \sigma =1.2\text{cm} \\ n=130 \\ {p}_0=P(16.5cm<x<18.1cm) \\ {p}_0=0.4949 \\ a=p_0\cdot n=0.4949\cdot 130=64 \end{gathered}$$

Use the normal distribution table.

$$\begin{gathered} p_1=P(x>17cm) \\ {p}_1=0.589 \\ b=p_1\cdot n=0.589\cdot 130=77 \end{gathered}$$

Use the normal distribution table.

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