A class test resulted in a mean score of 60% and a standard deviation of 15%. You scored 75%. Assuming the scores follow a normal distribution, and there are 200 in the class, how many students scored better than you? Give your answer to the nearest whole number.
Z-score = (X-μ)/σ
=(75-60)/15
=1
Look up normal distribution tables to find P(Z≥1)=0.8413
So 15.87% of students have better scores than 75%.
To find out how many students scored better than you, we need to calculate the z-score for your score and then use that z-score to find the proportion of students who scored better.
First, let's calculate the z-score using the formula:
z = (x - μ) / σ
where x is your score, μ is the mean score, and σ is the standard deviation.
In this case, your score (x) is 75%, the mean score (μ) is 60%, and the standard deviation (σ) is 15%.
z = (75% - 60%) / 15% = 1
Next, we need to find the proportion of students who scored better than you. We can use a standard normal distribution table (also known as a z-table) to find this proportion.
Looking up a z-score of 1 in the z-table, we find that the proportion of values to the left of z = 1 is approximately 0.8413. This means that approximately 84.13% of the class scored lower than you.
To find the number of students who scored better than you, we multiply this proportion by the total number of students in the class (200) and subtract it from the total number of students:
Number of students who scored better = (1 - 0.8413) * 200 ≈ 31.74
Rounding to the nearest whole number, approximately 32 students scored better than you.