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

Answer:

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

Step-by-step 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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(scores above 575)

P(x > 575)

$P( x > 575) = P( z > \displaystyle\frac{575 - 500}{50}) = P(z > 1.5)$

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

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.