Yuto works in the quality control department of a large company - Edexcel - A-Level Maths Statistics - Question 5 - 2017 - Paper 1

To find the probability that Yuto takes longer than 20 minutes, we first standardize the variable.

Using the formula for standardization: $z = \frac{X - \mu}{\sigma}$ where $X$ is the value we are interested in, $\mu$ is the mean, and $\sigma$ is the standard deviation.

For $X = 20$, $\mu = 18$, and $\sigma = 5$, we have: $z = \frac{20 - 18}{5} = \frac{2}{5} = 0.4$

Now, we find the probability: $P(T > 20) = P(Z > 0.4) = 1 - P(Z \leq 0.4)$ Using standard normal distribution tables or a calculator, we find: $P(Z \leq 0.4) \approx 0.6554$ Thus, $P(T > 20) = 1 - 0.6554 = 0.3446$