Question

1. the following histogram shows the weights of a number of frozen chickens in a supermarket. the weights are grouped such that ( 1 leq \text{weight} < 2 ), ( 2 leq \text{weight} < 3 ) and so on.

(a) find the total number of chickens.
(b) find the probability that this chicken weighs less than 3 kg.

Explanation:

Step1: Read frequencies from histogram

From the histogram:

• $1 \leq \text{weight} < 2$: 8 chickens
• $2 \leq \text{weight} < 3$: 22 chickens
• $3 \leq \text{weight} < 4$: 50 chickens
• $4 \leq \text{weight} < 5$: 12 chickens

Step2: Calculate total number of chickens

Sum all frequencies:
$8 + 22 + 50 + 12 = 92$

Step3: Find chickens <3kg

Sum frequencies for $1 \leq \text{weight} < 2$ and $2 \leq \text{weight} < 3$:
$8 + 22 = 30$

Step4: Compute probability for part (b)

Probability = $\frac{\text{Chickens <3kg}}{\text{Total chickens}}$ = $\frac{30}{92} = \frac{15}{46}$

Answer:

(a) 92
(b) $\frac{15}{46}$