In a process of manufacturing rubber flooring supports for cranes, it was verified by a quality control process that, on average, the type W support breaks when subjected to a weight of 6 tons, with a standard deviation of 1.2 tons .
The QA manager wants to know how likely a randomly selected carrier in the production line can withstand a weight of more than 7.9 tons.
Check the alternatives below that which answers the approximate percentage of the manager's question.
a) 8.7%
b) 7.7%
c) 6.7%
d) 4.7%
e) 5.7%
In these types of questions, a normal distribution is usually assumed. This is unrigorous for example because the "true" distribution in this case takes positive values only. This is a poor question, for that reason.
Divide the deviation from the mean by the standard deviation to get the number of standard deviations from the mean. Pull this value through an error function [1] to obtain the exact answer.
[1] https://en.wikipedia.org/wiki/Error_function