Respuesta :
Answer:
The approximate percentage of SAT scores that are less than 865 is 16%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 1060, standard deviation of 195.
Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865.
865 = 1060 - 195
So 865 is one standard deviation below the mean.
Approximately 68% of the measures are within 1 standard deviation of the mean, so approximately 100 - 68 = 32% are more than 1 standard deviation from the mean. The normal distribution is symmetric, which means that approximately 32/2 = 16% are more than 1 standard deviation below the mean and approximately 16% are more than 1 standard deviation above the mean. So
The approximate percentage of SAT scores that are less than 865 is 16%.
