Question

According to the College Board, SAT critical reading scores from the 2015 school year for high school students in the United States were normally distributed with a mean of 495 and a standard deviation of 116. Use a standard normal table such as this one to determine the probability that a randomly chosen high school student who took the SAT in 2015 will have a critical reading SAT score between 400 and 600 points. Give your answer as a percentage rounded to one decimal place

Answer 1

61.1% of high school student who took the SAT in 2015 will have a critical reading SAT score between 400 and 600 points.

Explanation:

We are given the following information in the question:

Mean, μ = 495

Standard Deviation, σ = 116

We are given that the distribution of scores from the 2015 school year for high school students in the United States is a bell shaped distribution that is a normal distribution.

Formula:

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

P(SAT score between 400 and 600 points)

`P(400 \leq x \leq 600) = P(\displaystyle(400 - 495)/(116) \leq z \leq \displaystyle(600-495)/(116)) = P(-0.818 \leq z \leq 0.905)\\\\= P(z \leq 0.905) - P(z < -0.818)\\= 0.8173 - 0.2064= 0.6109 \approx 61.1\%`

`P(400 \leq x \leq 600) = 61.1\%`

Thus, 61.1% of high school student who took the SAT in 2015 will have a critical reading SAT score between 400 and 600 points.