Question

In a standardized exam the mean score is 410 with an unknown standard deviation. Assume the scores follow a normal distribution. If 84.13 % of the students scored less than 430, what is the value of the standard deviation ?(round to a whole number)

Answer 1

The standard deviation of the scores on the standardized exam is 20 when 84.13% of students scored less than 430 and the mean score is 410.

Step-by-step explanation:

To find the standard deviation of the scores on the standardized exam, given that 84.13% of students scored less than 430 and the mean score is 410, we can use the concept of z-scores in a normal distribution. The z-score corresponding to 84.13% is approximately 1, because 84.13% is close to the percentage of data within one standard deviation above the mean in a normal distribution (about 84%).

The z-score formula is:

Z = (X - μ) / σ

Where X is the score in question, μ is the mean score, and σ is the standard deviation. We can rearrange the formula to solve for the standard deviation σ:

σ = (X - μ) / Z

Using the values X = 430, μ = 410, and Z = 1, we have:

σ = (430 - 410) / 1

σ = 20

Therefore, the standard deviation of the exam scores is 20 (rounded to the nearest whole number).