17 In 2019, the lengths of new-born babies at a clinic can be modelled by a normal distribution with mean 50 cm and standard deviation 4 cm .
17
- This normal distribution is represented in the diagram below.
Label the values 50 and 54 on the horizontal axis.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{deec0d32-b031-4227-bc80-7150a0acbc94-29_375_531_644_817}
\captionsetup{labelformat=empty}
\caption{Length (cm)}
\end{figure}
17 - State the probability that the length of a new-born baby is less than 50 cm .
17 - Find the probability that the length of a new-born baby is more than 56 cm .
17 - Find the probability that the length of a new-born baby is more than 40 cm but less than 60 cm .
17 - Determine the length exceeded by 95\% of all new-born babies at the clinic.
17 - In 2020, the lengths of 40 new-born babies at the clinic were selected at random.
The total length of the 40 new-born babies was 2060 cm .
Carry out a hypothesis test at the \(10 \%\) significance level to investigate whether the mean length of a new-born baby at the clinic in 2020 has increased compared to 2019.
You may assume that the length of a new-born baby is still normally distributed with standard deviation 4 cm .