To determine the correct statement about the data set with a mean of 200 and a standard deviation of 10, we can consider the properties of the normal distribution (assuming the data is normally distributed for the sake of argument).
- Range of Values: In a normally distributed data set, approximately 68% of the values lie within one standard deviation of the mean. This means that approximately 68% of the data will fall within the interval \([190, 210]\) (which is the mean ± one standard deviation).
Given that:
- Mean = 200
- Standard deviation = 10
Evaluating the Statements:
-
A value chosen randomly from the data set will typically be contained in the interval [190, 210]: This is correct as it includes one standard deviation above and below the mean.
-
A value chosen randomly from the data set will typically be contained in the interval [200, 210]: This statement only covers half of the interval of one standard deviation above the mean, which does not represent a typical range of values.
-
A value chosen randomly from the data set will typically be contained in the interval [-20, 20]: This interval does not make sense given the mean of 200; it is not a typical range for data values.
-
A value chosen randomly from the data set will typically be contained in the interval [180, 200]: Like the second statement, this only considers part of the typical range but does not include values significantly above the mean.
Conclusion:
The correct statement is:
A value chosen randomly from the data set will typically be contained in the interval [190, 210].