Answer :
To determine how many scores were at or below 90, knowing that a score of 90 represents the 55th percentile out of 102 exams, we can follow these steps:
1. Understand the Percentile: A score at the 55th percentile means that 55% of the scores are less than or equal to that score. Therefore, 90 is higher than or equal to 55% of the scores.
2. Calculate Percentile of Total Exams: We need to find out how many exams fall at or below that 55th percentile. This is done by taking 55% of the total number of exams.
[tex]\[ \text{Number of exams at or below 90} = \left(\frac{55}{100}\right) \times 102 \][/tex]
3. Perform Multiplication:
[tex]\[ \left(\frac{55}{100}\right) \times 102 = 0.55 \times 102 \][/tex]
4. Calculate the Product:
[tex]\[ 0.55 \times 102 = 56.1 \][/tex]
5. Round to the Nearest Whole Number: Since we can't have a fraction of an exam, we round the result to the nearest whole number.
[tex]\[ 56.1 \approx 56 \][/tex]
Therefore, there were approximately 56 scores that were at or below 90.
1. Understand the Percentile: A score at the 55th percentile means that 55% of the scores are less than or equal to that score. Therefore, 90 is higher than or equal to 55% of the scores.
2. Calculate Percentile of Total Exams: We need to find out how many exams fall at or below that 55th percentile. This is done by taking 55% of the total number of exams.
[tex]\[ \text{Number of exams at or below 90} = \left(\frac{55}{100}\right) \times 102 \][/tex]
3. Perform Multiplication:
[tex]\[ \left(\frac{55}{100}\right) \times 102 = 0.55 \times 102 \][/tex]
4. Calculate the Product:
[tex]\[ 0.55 \times 102 = 56.1 \][/tex]
5. Round to the Nearest Whole Number: Since we can't have a fraction of an exam, we round the result to the nearest whole number.
[tex]\[ 56.1 \approx 56 \][/tex]
Therefore, there were approximately 56 scores that were at or below 90.
