To be able to determine the expected number of students who would choose spring as their favorite season, let's determine the possible ratio based on the given table.
![\frac{\text{ Number of students choosing spring}}{\text{ Total number of students in the survey}}\text{ = }\frac{\text{ }24}{24\text{ + 55 + }12\text{ + 9}}](https://img.qammunity.org/2023/formulas/mathematics/college/6313o2bpruc1cravax0q1zlthetj7aqs76.png)
![\text{ }(24)/(100)\text{ = 0.24}](https://img.qammunity.org/2023/formulas/mathematics/college/k1t3q28z2g4iyt8y9yxwc8n5ads5fnqcaz.png)
Let's now determine the expected number based on the ratio of the sample in the survey,
Out of 1,300 students,
![\text{ 1,300 x 0.24 = }312](https://img.qammunity.org/2023/formulas/mathematics/college/gnreiwv9tp3p1r7wstpycsliejve4sz6kq.png)
Therefore, the answer is 312.