Let x be the random variable representing the test score of a student. Since the scores are normally distributed and the population mean and standard deviation are known, we would apply the formula which is expressed as
z = (x - mean)/standard deviation
From the information given,
mean = 82
standard deviation = 5.85
For a student that scored below 71, the probability is expressed as
P(x < 71)
We would find the z score using the formula stated above
x = 71
z = (71 - 82)/5.85 = - 1.88
We would find the probability value corresponding to a z score of - 1.88 from the normal distribution table. The value is 0.03
Thus,
P(x < 71) = 0.03
Since there are 40 students in the class, the number of students that scored below 71 would be
0.03 * 40
= 1.2
That is approximately 1 student
The correct option is the second one