Question

On a standardized test with a normal distribution, the mean is 75 and the standard deviation is 3. Approximately 95% of the scores lie within which interval?

A) 72 to 78
B) 63 to 87
C) 69 to 81
D) 66 to 84

Answer 1

Approximately 95% of the scores lie within the interval of 69 to 81. Hence the correct answer is option C

Step-by-step explanation:

To find the interval within which approximately 95% of the scores lie, we can use the empirical rule for normal distributions. The empirical rule states that about 68% of the scores lie within one standard deviation of the mean, about 95% lie within two standard deviations, and about 99.7% lie within three standard deviations.

Since the mean is 75 and the standard deviation is 3, two standard deviations above and below the mean would be 75 - 2(3) and 75 + 2(3), or 69 and 81, respectively. Therefore, approximately 95% of the scores lie within the interval 69 to 81. Therefore, the answer is C) 69 to 81.