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Bridies' Bearing Works manufactures bearing shafts whose diameters are normally distributed with parameters <math>\mu = 1</math>, <math>\sigma = .002</math>. The buyer's specifications require these diameters to be <math>1.000 \pm .003</math> cm. If the manufacturer improves her quality control, she can reduce the value of <math>\sigma</math>. | Bridies' Bearing Works manufactures bearing shafts whose diameters are normally distributed with parameters <math>\mu = 1</math>, <math>\sigma = .002</math>. The buyer's specifications require these diameters to be <math>1.000 \pm .003</math> cm. If the manufacturer improves her quality control, she can reduce the value of <math>\sigma</math>. Find the greatest value of <math>\sigma</math> that will ensure that no more than 1 percent of her shafts are likely to be rejected? | ||
shafts are likely to be rejected? | |||
<ul class="mw-excansopts"> | |||
<li> 12.9 * 10<sup>-3</sup> </li> | |||
<li>13.28 * 10 <sup>-3</sup></li> | |||
<li>13.6 * 10 <sup>-3</sup></li> | |||
<li>14 * 10 <sup>-3</sup></li> | |||
<li>14.28 * 10 <sup>-3 </sup></li> | |||
</ul> | |||
'''References''' | '''References''' | ||
{{cite web |url=https://math.dartmouth.edu/~prob/prob/prob.pdf |title=Grinstead and Snell’s Introduction to Probability |last=Doyle |first=Peter G.|date=2006 |access-date=June 6, 2024}} | {{cite web |url=https://math.dartmouth.edu/~prob/prob/prob.pdf |title=Grinstead and Snell’s Introduction to Probability |last=Doyle |first=Peter G.|date=2006 |access-date=June 6, 2024}} | ||
Latest revision as of 21:12, 26 June 2024
Bridies' Bearing Works manufactures bearing shafts whose diameters are normally distributed with parameters [math]\mu = 1[/math], [math]\sigma = .002[/math]. The buyer's specifications require these diameters to be [math]1.000 \pm .003[/math] cm. If the manufacturer improves her quality control, she can reduce the value of [math]\sigma[/math]. Find the greatest value of [math]\sigma[/math] that will ensure that no more than 1 percent of her shafts are likely to be rejected?
- 12.9 * 10-3
- 13.28 * 10 -3
- 13.6 * 10 -3
- 14 * 10 -3
- 14.28 * 10 -3
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.