Given that on one section of the SAT the mean is 500 and the standard deviation is 100, what is the approximate probability of a student scoring 700 or higher on the test?
A)0.98
B)0.02
C)0.12
D)0.75

Question

Given that on one section of the SAT the mean is 500 and the standard deviation is 100, what is the approximate probability of a student scoring 700 or higher on the test?​
A)0.98
B)0.02
C)0.12
D)0.75

Quizplus · Accepted Answer

To solve this problem, we need to use the standard normal distribution, where the mean is 0 and the standard deviation is 1. We can convert the given values using the formula:

Z = (X - μ) / σ

where X is the score we're interested in (700 or higher), μ is the mean (500), and σ is the standard deviation (100).

Z = (700 - 500) / 100
Z = 2

Now we look up the probability of Z being greater than 2 in a standard normal distribution table or calculator, which is approximately 0.0228.

However, since we are interested in the probability of scoring 700 or higher (which includes all scores greater than 700), we need to subtract the probability of scoring between 500 and 700 from 1. This can also be looked up in the standard normal distribution table or calculated as:

Z = (500 - 500) / 100
Z = 0

Z = (700 - 500) / 100
Z = 2

P(700 or higher) = 1 - P(500 ≤ X ≤ 700)
P(500 ≤ X ≤ 700) = P(Z ≤ 2) - P(Z ≤ 0)
P(500 ≤ X ≤ 700) = 0.9772 - 0.5
P(500 ≤ X ≤ 700) = 0.4772

P(700 or higher) = 1 - 0.4772
P(700 or higher) = 0.5228 or approximately 0.02

Therefore, the answer is B) 0.02.

Given That on One Section of the SAT the Mean