Answer:
The percentage of students who scored less than 400 is 16%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
[tex]\mu = 500, \sigma = 100[/tex]
Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 400.
400 = 500 - 100
So 400 is one standard deviation below the mean.
By the Empirical Rule, 68% of the students scored within 1 standard deviation of the mean, that is, within 400 and 600. The other 32% scores were more than 1 standard deviation from the mean. Since the normal distribution is symmetric, 16% scored more than one standard deviation below the mean(less than 400) and 16% scored more than one standard deviation above the mean(more than 600). So
The percentage of students who scored less than 400 is 16%.
