Answer:
a. About 64
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed 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:
Mean = 70
Standard deviation = 5
Use the empirical rule to determine the number of students who scored less than 65 or more than 75?
65 = 70 - 5
So 65 is one standard deviation below the mean
75 = 70 + 5
So 75 is one standard deviation above the mean.
By the Empirical Rule, 68% of the students scored between 65 and 75. The other 100-68 = 32% scored less than 65 or more than 75.
Out of 200, that is
0.32*200 = 64
So the correct answer is:
a. About 64
