Javelin throwers

Javelin throwers Anna and Barbora have average throw lengths of 67 m and 75 m, respectively, and standard deviations of 6 m and 3 m, respectively. Assume that the throw lengths have independent normal distributions. Calculate the probability that Anna throws further than Barbora in one throw.

Correct answer:

p =  0.1165

Step-by-step explanation:

$$\begin{gathered} {\mu }_1=67\text{m} \\ {\sigma }_1=6\text{m} \\ {\mu }_2=75\text{m} \\ {\sigma }_2=3\text{m} \\ A-B=A+(-1)\cdot B \\ {\mu }_3={\mu }_1-{\mu }_2=67-75=-8\text{m} \\ {\sigma }_3=\sqrt{{\sigma }_1^2+{\sigma }_2^2}=\sqrt{6^2+3^2}=3\sqrt{5}\text{m}\doteq 6.7082\text{m} \\ p=N({\mu }_3,{\sigma }_3)>0 \\ p=0.1165 \end{gathered}$$

Use the normal distribution table.

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