1. **State the problem:** We have a cumulative frequency curve for the lengths of 80 bananas. We want to find: a) The interquartile range (IQR) of the banana lengths. b) The fraction of bananas with lengths between 13 cm and 20 cm. 2. **Find the interquartile range (IQR):** - The IQR is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). - Since there are 80 bananas, $Q_1$ corresponds to the 20th banana (25% of 80) and $Q_3$ corresponds to the 60th banana (75% of 80). - From the cumulative frequency curve: - At length 13 cm, cumulative frequency is about 15 bananas. - At length 20 cm, cumulative frequency is about 60 bananas. - To find $Q_1$ (20th banana): - 15 bananas have length ≤ 13 cm. - The 20th banana lies just after 13 cm. - By estimating from the curve, $Q_1$ is approximately 14 cm. - To find $Q_3$ (60th banana): - The 60th banana corresponds to length 20 cm. - Therefore, $$IQR = Q_3 - Q_1 = 20 - 14 = 6 \text{ cm}.$$ 3. **Estimate the fraction of bananas with lengths between 13 cm and 20 cm:** - From the curve, cumulative frequency at 13 cm is about 15 bananas. - At 20 cm, cumulative frequency is about 60 bananas. - Number of bananas between 13 cm and 20 cm is $60 - 15 = 45$. - Fraction of bananas the shop buys is: $$\frac{45}{80} = 0.5625.$$ - So approximately 56.25% of the bananas are bought by the shop. **Final answers:** - a) Interquartile range is 6 cm. - b) Fraction of bananas bought is approximately 0.56 (56%).