A dataset with mean 85 and standard deviation 11 has a symmetric bell-shaped distribution. Find an interval that is likely about $$ 95 \% $$ of the data values. Enter exact answers.

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Given a dataset with a mean of $$ 85 $$ and a standard deviation of $$ 11 $$, and knowing that the distribution is symmetric and bell-shaped, we can apply the empirical rule (68-95-99.7 rule). This rule states that approximately $$ 95\% $$ of the data in a normally distributed dataset lies within two standard deviations of the mean.

To find the interval:

1. **Calculate two standard deviations:**
   $$
   2 \times 11 = 22
   $$

2. **Determine the lower bound of the interval:**
   $$
   85 - 22 = 63
   $$

3. **Determine the upper bound of the interval:**
   $$
   85 + 22 = 107
   $$

Therefore, the interval that likely contains about $$ 95\% $$ of the data values is:

$$
63 \leq x \leq 107
$$

**Answer:** $$63 \leq x \leq 107$$
The interval containing about 95% of the data values is from 63 to 107.

A dataset with mean 85 and standard deviation 11 has a symmetric bell-shaped distribution. Find an interval that is likely about \( 95 \% \) of the data values. Enter exact answers.

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