Answer:
0.0002 inch
Step-by-step explanation:
The empirical rule of the normal distribution, the 68-95-99.7 rule, means
if the mean is <em>μ</em> and the standard deviation is <em>σ</em>,
68% of data lies within <em>μ </em>- <em>σ</em> and <em>μ </em>+ <em>σ</em>,
95% of data lies within <em>μ </em>- 2<em>σ</em> and <em>μ </em>+ 2<em>σ</em>,
99.7% of data lies within <em>μ </em>- 3<em>σ</em> and <em>μ </em>+ 3<em>σ.</em>
<em />
From the question, <em>μ</em> = 0.002.
The required range is 0.0014 to 0.0026.
With a probability of 0.9963, then 0.9963 × 100% = 99.63% should lie within the range. This approximately corresponds to <em>μ </em>- 3<em>σ</em> and <em>μ </em>+ 3<em>σ.</em>
<em>μ </em>- 3<em>σ</em> = 0.0014
0.002 - 3<em>σ</em> = 0.0014
3<em>σ</em> = 0.0006
<em>σ</em> = 0.0002
Hence, the standard deviation is 0.0002 inch
We can check with the other end of the range:
<em>μ </em>+ 3<em>σ</em> = 0.0026
3<em>σ</em> = 0.0026 - 0.002
3<em>σ</em> = 0.0006
<em>σ</em> = 0.0002
