Question

mrs. allen surveys a random sample of 200 juniors. she asks students to describe their dream car as a sports car, suv, truck, or sedan.
part a
mrs. allen organized some of the results in a two - way relative frequency table for dream cars of students by driver’s license status. complete the table by entering the relative frequencies.

	sports car	suv	truck	sedan	total
has a license	\\(\square\\)	\\(\square\\)	\\(\frac{32}{200}=0.16\\)	\\(\square\\)	\\(\square\\)
total	\\(\frac{59}{200}=0.295\\)	\\(\frac{45}{200}=0.225\\)	\\(\square\\)	\\(\frac{40}{200}=0.20\\)	\\(\frac{200}{200}=1.00\\)

part b
select an answer from each drop - down list to make each statement true
among the students in the sample who do not have a driver’s license, a \\(\text{select}\\) (options: sports car, suv, truck, sedan) is the most popular dream car.

Explanation:

Step1: Complete "Does Not Have a License" - SUV

The total for "Does Not Have a License" is 0.30. Sum of known relative frequencies: \(0.075 + 0.12 + 0.06 = 0.255\). So SUV relative frequency: \(0.30 - 0.255 = 0.045\) (or \(\frac{9}{200}=0.045\)).

Step2: Complete "Total" - Truck

Sum of Truck relative frequencies: \(0.12 + 0.16 = 0.28\) (or \(\frac{24 + 32}{200}=\frac{56}{200}=0.28\)).

Step3: Complete "Has a License" - Sports Car

Total Sports Car: 0.295. Subtract "Does Not Have a License" (0.075): \(0.295 - 0.075 = 0.22\) (or \(\frac{59 - 15}{200}=\frac{44}{200}=0.22\)).

Step4: Complete "Has a License" - SUV

Total SUV: 0.225. Subtract "Does Not Have a License" (0.045): \(0.225 - 0.045 = 0.18\) (or \(\frac{45 - 9}{200}=\frac{36}{200}=0.18\)).

Step5: Complete "Has a License" - Sedan

Total Sedan: 0.20. Subtract "Does Not Have a License" (0.06): \(0.20 - 0.06 = 0.14\) (or \(\frac{40 - 12}{200}=\frac{28}{200}=0.14\)).

Step6: Complete "Has a License" - Total

Total students: 1.00. Subtract "Does Not Have a License" (0.30): \(1.00 - 0.30 = 0.70\) (or \(\frac{200 - 60}{200}=\frac{140}{200}=0.70\)).

Step7: Part B - Most Popular (No License)

Compare relative frequencies for "Does Not Have a License": Sports Car (0.075), SUV (0.045), Truck (0.12), Sedan (0.06). The largest is 0.12 (Truck? Wait, no—wait, wait, earlier SUV calculation: Wait, no, wait the "Does Not Have a License" row: Sports Car 0.075, SUV we found 0.045, Truck 0.12, Sedan 0.06. Wait, but wait, maybe I made a mistake. Wait, the total for "Does Not Have a License" is 60/200=0.30. 15 (Sports) +? (SUV) +24 (Truck) +12 (Sedan) = 60. So 15 + x +24 +12 =60 → x=9. So SUV is 9/200=0.045. Then the frequencies: 0.075 (Sports), 0.045 (SUV), 0.12 (Truck), 0.06 (Sedan). Wait, but 0.12 is Truck? But wait, maybe the question is about "most popular"—wait, no, maybe I miscalculated. Wait, no, the "Does Not Have a License" row: Sports (15), SUV (9), Truck (24), Sedan (12). So Truck has 24, which is the highest in that row. Wait, but 24/200=0.12, which is higher than 15 (0.075), 9 (0.045), 12 (0.06). So Truck? Wait, but let's check again. Wait, the problem says "Among the students in the sample who do not have a driver’s license, a [blank] is the most popular dream car." So we look at the "Does Not Have a License" row: Sports Car (0.075), SUV (0.045), Truck (0.12), Sedan (0.06). So the highest is Truck (0.12). Wait, but maybe I messed up the SUV calculation. Wait, 15 + SUV +24 +12 =60 → SUV=9. So 9/200=0.045. So yes, Truck is 0.12, which is higher than others. Wait, but let's confirm the numbers: 15 (Sports) +9 (SUV) +24 (Truck) +12 (Sedan) = 60, which matches the total 60/200=0.30. So among those without license, Truck has the highest relative frequency (0.12) among the four. Wait, but wait, 24 is more than 15, 9, 12. So yes, Truck. But wait, maybe the original table had a typo? No, following the numbers: 15, 9, 24, 12. So Truck is 24, which is the largest. So the most popular is Truck.

For Part A table completion:

• Does Not Have a License - SUV: \( \frac{9}{200} = 0.045 \)
• Total - Truck: \( \frac{56}{200} = 0.28 \)
• Has a License - Sports Car: \( \frac{44}{200} = 0.22 \)
• Has a License - SUV: \( \frac{36}{200} = 0.18 \)
• Has a License - Sedan: \( \frac{28}{200} = 0.14 \)
• Has a License - Total: \( \frac{140}{200} = 0.70 \)

Answer:

(Part A Table Cells):

• Does Not Have a License - SUV: \( \boldsymbol{0.045} \) (or \( \frac{9}{200} \))
• Total - Truck: \( \boldsymbol{0.28} \) (or \( \frac{56}{200} \))
• Has a License - Sports Car: \( \boldsymbol{0.22} \) (or \( \frac{44}{200} \))
• Has a License - SUV: \( \boldsymbol{0.18} \) (or \( \frac{36}{200} \))
• Has a License - Sedan: \( \boldsymbol{0.14} \) (or \( \frac{28}{200} \))
• Has a License - Total: \( \boldsymbol{0.70} \) (or \( \frac{140}{200} \))