The mean Algebra 2 test score is 81.5, with a standard deviation of 5.1. There are 130 students taking the course. Assuming a normally distributed curve, how many students scored below 76.4?

Step-by-step explanation:

Let x be the random variable representing the algebra test scores of the students. 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 = 81.5

σ = 5.1

the probability that a student scores below 76.4 is expressed as

P (x ≤ 76.4)

For x = 76.4

z = (76.4 - 81.5) / 5.1 = - 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

For x = 8

z = (8 - 6) / 1 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.159

Therefore, the number of students that scored below 76.4 is

0.159 * 130 = 21 students