The scores of students on standardized test are normally distributed with a mean of 300 and a standard deviation of 40. Between what two values do 99.7% of the test scores lie?
To find the range within which 99.7% of the test scores lie, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normally distributed dataset:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the mean is 300 and the standard deviation is 40, we can calculate the range for 99.7% of the test scores as follows:
Lower Bound = Mean - (3 * Standard Deviation)
Upper Bound = Mean + (3 * Standard Deviation)
Lower Bound = 300 - (3 * 40)
Lower Bound = 300 - 120
Lower Bound = 180
Upper Bound = 300 + (3 * 40)
Upper Bound = 300 + 120
Upper Bound = 420
Therefore, 99.7% of the test scores lie between the values of 180 and 420.
To determine between what two values do 99.7% of the test scores lie, we can use the empirical rule, also known as the 68-95-99.7 rule, which applies to data that follows a normal distribution.
The empirical rule states that:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, we know that the mean is 300, and the standard deviation is 40.
To find the range within which 99.7% of the test scores lie, we need to go three standard deviations above and below the mean.
Lower Bound:
300 - (3 * 40) = 300 - 120 = 180
Upper Bound:
300 + (3 * 40) = 300 + 120 = 420
Therefore, between 180 and 420, approximately 99.7% of the test scores will lie.
181.278 and 418.722
not sure how you want to round them