3 Apples are sold in bags of 5. Based on her previous experience, Freya claims that the probability of any apple weighing more than 100 grams is 0.35 , independently of other apples in the bag.

The apples in a random sample of 150 bags are checked and the number, $x$, in each bag weighing more than 100 grams is recorded. The results are shown in the following table.

\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
$x$ & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
Frequency & 12 & 39 & 46 & 37 & 12 & 4 \\
\hline
\end{tabular}
\end{center}

Carry out a goodness of fit test at the $5 \%$ significance level and hence comment on Freya's claim.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2020 Q3}}