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.
| \(x\) | 0 | 1 | 2 | 3 | 4 | 5 |
| Frequency | 12 | 39 | 46 | 37 | 12 | 4 |
Carry out a goodness of fit test at the \(5 \%\) significance level and hence comment on Freya's claim.