Question

According to the data, the mean quantitative score on a standardized test for female college-bound high school seniors was 500. The scores are approximately Normally distributed with a population standard deviation of 50. What percentage of the female college-bound high school seniors had scores above 575?

Answer 1

6.68% of the female college-bound high school seniors had scores above 575.

Explanation:

We are given the following information in the question:

Mean, μ = 500

Standard Deviation, σ = 50

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(scores above 575)

P(x > 575)

`P( x > 575) = P( z > \displaystyle(575 - 500)/(50)) = P(z > 1.5)`

`= 1 - P(z \leq 1.5)`

Calculation the value from standard normal z table, we have,

`P(x > 575) = 1 - 0.9332= 0.0668 = 6.68\%`

6.68% of the female college-bound high school seniors had scores above 575.