For a normally distributed set of scores with, what is the probability of a score being equal to or less than 200? $$\mu = 200 \text { and } \sigma = 20$$
A).3413
B).6826
C).5000
D).9544

Question

Quizplus · Accepted Answer

Since the distribution is normal, we can use the empirical rule to estimate probabilities. The empirical rule states that 68% of the scores fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Since our mean is 200 and our standard deviation is 20, one standard deviation below the mean is 180. To find the probability of a score being equal to or less than 200, we need to find the proportion of scores that lie to the left of 200, which is the same as the proportion of scores that lie within one standard deviation of the mean. According to the empirical rule, this is 68%. Therefore, the answer is C).

For a Normally Distributed Set of Scores With, What Is μ=200 and σ=20\mu = 200 \text { and } \sigma = 20μ=200 and σ=20

For a Normally Distributed Set of Scores With, What Is $\mu = 200 \text { and } \sigma = 20$