Chapter 11 Data Analysis and Statistics - 11.3 Use Normal Distributions - 11.3 Exercises - Skill Practice - Page 760: 10

$4.7\%$

As we can see these are half the elements that are between $2$ and $3$ standard deviations away from the mean. The normal distribution is symmetric about the mean; thus using the 68-95-99.7 rule and the graph we get: $P(\overline{x}-3\sigma\leq x\leq \overline{x}-2\sigma\cup \overline{x}+2\sigma\leq x\leq \overline{x}+3\sigma)=2.35\%+2.35\%=4.7\%$