Question

In a math aptitude test, students scores are found to be normally distributed having mean as 45 and standard deviation 5. What percent of students scored more than the mean score?

• A. 45%
• B. 50%
• C. 5%
• D. 60%

Hint:

A normal curve is symmetric about the mean, so half of the area lies above it.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A normal distribution is symmetric about its mean. The bell shaped curve has the same area on both sides of the mean. The total area under the curve is 1, or 100%.

Step 2: Apply the symmetry.
The mean score is 45. The area to the left of 45 equals the area to the right of 45. So each area is half of 100%, that is 50%.

Step 3: Check with the z score.
For score 45, \(z = \frac{45-45}{5} = 0\). So \(P(X>45)=P(Z>0)=0.5\), which is 50%.

Step 4: Check the other options.
45%, 5% and 60% cannot be right, because the mean is the exact centre of the curve. The standard deviation 5 does not change this answer.

Final Answer:
50% of the students scored more than the mean. \[ \boxed{50\%} \]