the mean and standard deviation of the grades of 500 students who took an maths exam were 69 and 7 respectively. if the grades have a bell shaped distribution, how many of these students received a grade of more than 83 marks?

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to this Z score. Multiply it by 500.

thanks.

To determine how many students received a grade of more than 83 marks, we need to use the concept of standard deviation and the bell-shaped distribution.

Step 1: Understanding the information given
We are given that the mean (μ) of the grades is 69 and the standard deviation (σ) is 7.

Step 2: Z-score calculation
To find the number of students who received a grade higher than 83 marks, we need to calculate the z-score.

Z-score (Z) = (X - μ) / σ

where X is the value we want to know the relative position of, μ is the mean, and σ is the standard deviation.

In this case, X = 83, μ = 69, and σ = 7. Plugging these values into the formula, we get:

Z = (83 - 69) / 7
Z = 2

Step 3: Convert Z-score to percentage
The Z-score tells us how many standard deviations the value is from the mean. We can use a Z-score table or a calculator to find the percentage of values that fall above a given Z-score.

Using a Z-score table (or a calculator), we find that a Z-score of 2 corresponds to a percentage of approximately 97.72%.

Step 4: Calculating the number of students
To find the number of students who received a grade of more than 83 marks, we can multiply the percentage obtained in Step 3 by the total number of students (500).

Number of students = Percentage above Z * Total number of students

Number of students = 0.9772 * 500
Number of students ≈ 488.6

Therefore, approximately 489 students received a grade of more than 83 marks.