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