Question

a group of 100 students were asked if they study french or spanish in school. the results are shown in this two - way table. which statements are correct? check all that apply. 5 students study both french and spanish. 63 students study french. 2 students study neither french nor spanish. 30 students study french, but not spanish. 63 students study spanish.

Explanation:

Step1: Check the intersection cell

The number of students who study both French and Spanish is the value in the cell where 'Spanish' and 'French' intersect, which is 5. So the statement "5 students study both French and Spanish" is correct.

Step2: Calculate French - only students

The number of students who study French but not Spanish is the value in the 'French' and 'Not Spanish' cell, which is 30. So the statement "30 students study French, but not Spanish" is correct.

Step3: Check non - French and non - Spanish students

The number of students who study neither French nor Spanish is the value in the 'Not French' and 'Not Spanish' cell, which is 2. So the statement "2 students study neither French nor Spanish" is correct.

Step4: Check French students total

The total number of students who study French is 35 (sum of students who study French and Spanish and French and not Spanish), not 63. So the statement "63 students study French" is incorrect.

Step5: Check Spanish students total

The total number of students who study Spanish is 68, not 63. So the statement "63 students study Spanish" is incorrect.

Answer:

5 students study both French and Spanish.
2 students study neither French nor Spanish.
30 students study French, but not Spanish.