b) Electric cable is sold in reels. The length of cable on the reels can be assumed to follow a Normal distribution with mean 50 metres and standard deviation 0.5 metres.
$11.9 \%$ of reels have more than $x$ metres of cable.
Find the value of $x$.
Answer
Final Answer: The value of \(x\) is approximately \(\boxed{50.59}\).
Step 1 ：The problem is asking for the value of \(x\) such that \(11.9\%\) of the reels have more than \(x\) meters of cable. This is a problem of finding the percentile of a normal distribution.
Step 2 ：The mean (\(\mu\)) is 50 and the standard deviation (\(\sigma\)) is 0.5.
Step 3 ：We know that \(11.9\% = 0.119\) is the right tail of the distribution, so we need to find the \(100\% - 11.9\% = 88.1\%\) percentile of the distribution.
Step 4 ：We can use the inverse of the cumulative distribution function (CDF) of the normal distribution, also known as the quantile function, to find this value.
Step 5 ：Using the given values, we find that \(x = 50.59000027017387\).
Step 6 ：Final Answer: The value of \(x\) is approximately \(\boxed{50.59}\).
