Answer :
Final answer:
About 95% of IQ scores are between 77 and 129 for a bell-shaped distribution with a mean of 103 and a standard deviation of 13, according to the empirical rule.
Explanation:
In the context of a bell-shaped distribution of IQ scores with a mean of 103 and a standard deviation of 13, we can use the empirical rule to estimate the range in which approximately 95% of IQ scores are likely to fall. This rule states that in a normal distribution, roughly 95% of data falls within two standard deviations of the mean. In this case, we calculate two standard deviations as 2 * 13 = 26. Therefore, to find the range, we add and subtract 26 from the mean, 103.
The lowest value of the range is 103 - 26 = 77, and the highest is 103 + 26 = 129. Therefore, approximately 95% of IQ scores would lie between 77 and 129, which corresponds to option (a).
