# Chapter 11 Data Analysis and Statistics - 11.3 Use Normal Distributions - 11.3 Exercises - Skill Practice - Page 760: 12

$49.85\%$

#### Work Step by Step

$\text{z-score}=\frac{\text{data item-mean}}{\text{standard deviation}}$ $|\frac{45-29}{4}|=3$, thus these are half the elements that are $3$ 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: $P(\overline{x}\leq x\leq\overline{x}+3\sigma)=34\%+13.5\%+2.35\%=49.85\%$

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