Answer :
The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.
In statistics, understanding and interpreting data is an essential skill. One way to interpret data is by analyzing the distribution of values within a certain range.
To determine whether the statement is true or false, we need to analyze the distribution of boy's heights between the two ranges. Assuming the heights of boys are normally distributed, we can use the empirical rule, also known as the 68-95-99.7 rule, to estimate the percentage of boys within each range.
The empirical rule states that in a normal distribution:
68% of the values fall within one standard deviation of the mean
95% of the values fall within two standard deviations of the mean
99.7% of the values fall within three standard deviations of the mean
We can use this rule to estimate the percentage of boys within each range as follows:
Between 167 and 169: This range is one standard deviation below the mean. Therefore, approximately 68% of boys' heights fall within this range.
Between 169 and 170: This range is between one and two standard deviations below the mean. Therefore, approximately 27% of boys' heights fall within this range.
Based on this analysis, we can see that there are not approximately as many boys between 167 and 169 as there are between 169 and 170. In fact, there are significantly more boys between 167 and 169 than there are between 169 and 170.
The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.
To know more about Normal Distribution here
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