Answer:
49.85% of ITBS scores are between 3 and 12
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 = 12
Standard deviation = 3
The normal distribution is symmetric, which means that 50% of the scores are below the mean and 50% are below.
What percent of ITBS scores are between 3 and 12
12 is the mean
3 = 12 - 3*3
3 is three standard deviations below the mean.
By the Empirical Rule, of the 50% of the measures which are below the mean(below 12), 99.7% are within 3 standard deviations of the mean, that is, above 3.
So
p = 0.5*0.997 = 0.4985
49.85% of ITBS scores are between 3 and 12
