Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118. If a recent test-taker is selected at random, what is the probability the student scored 573 or greater on the exam?

Answer: the probability that the student scored 573 or greater on the exam is 0.31

Step-by-step explanation:

Let x be the random variable representing the math scores on the SAT exam. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ) / σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 514

σ = 118

the probability that the student scored 573 or greater on the exam is expressed as

P (x > 573) = 1 - P (x ≤ 573

For x = 573,

z = (573 - 514) / 118 = 0.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.69

P (x > 573) = 1 - 0.69 = 0.31