The problem provides a table showing the masses of 40 parcels in a warehouse. The masses are grouped into intervals, with corresponding frequencies. Part (iii) asks to find the probability that a randomly selected parcel has a mass of 2 kg or less.

1. Problem Description

The problem provides a table showing the masses of 40 parcels in a warehouse. The masses are grouped into intervals, with corresponding frequencies. Part (iii) asks to find the probability that a randomly selected parcel has a mass of 2 kg or less.

2. Solution Steps

To find the probability, we need to determine the number of parcels with a mass of 2 kg or less, and divide it by the total number of parcels, which is

4

0. The parcels with a mass of 2 kg or less are in the intervals $0.5 < m \le 1$ and $1 < m \le 2$. The frequencies for these intervals are 4 and 7, respectively. So, the total number of parcels with a mass of 2 kg or less is $4 + 7 = 11$. Therefore, the probability is the number of parcels with mass less than or equal to 2 kg divided by the total number of parcels.

Probability = $\frac{\text{Number of parcels with mass } \le 2 \text{ kg}}{\text{Total number of parcels}}$

Probability = $\frac{4+7}{40}$

Probability = $\frac{11}{40}$

3. Final Answer

$\frac{11}{40}$