3 The number of customers who visit a particular shop between 9.00 am and 10.00 am has the distribution \(\operatorname { Po } ( \lambda )\). In the past the value of \(\lambda\) was 5.2. Following some new advertising, the manager wishes to test whether the value of \(\lambda\) has increased. He chooses a random sample of 20 days and finds that the total number of customers who visited the shop between 9.00 am and 10.00 am on those days is 125 . Use an approximating distribution to test at the \(2.5 \%\) significance level whether the value of \(\lambda\) has increased.

3 The number of customers who visit a particular shop between 9.00 am and 10.00 am has the distribution $\operatorname { Po } ( \lambda )$. In the past the value of $\lambda$ was 5.2. Following some new advertising, the manager wishes to test whether the value of $\lambda$ has increased. He chooses a random sample of 20 days and finds that the total number of customers who visited the shop between 9.00 am and 10.00 am on those days is 125 .

Use an approximating distribution to test at the $2.5 \%$ significance level whether the value of $\lambda$ has increased.\\

\hfill \mbox{\textit{CAIE S2 2020 Q3}}