excans:F31dee52f9: Difference between revisions
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(Created page with "'''Solution: B''' We need to find <math>\sigma </math> small enough so that the range of values outside <math>1.000 \pm .003</math> cm has probability less than or equal to 1%. If <math>X</math> has a normal distribution with mean 1 and standard deviation <math>\sigma </math> then <math display = "block"> P(X \in 1.000 \pm .003 ) = P(Z \in \pm 0.003/\sigma ) \geq 0.99 = P(Z \in \pm 2.576) </math> where <math>Z </math> is a standard normal. Hence we need <math>\sigma...") |
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where <math>Z </math> is a standard normal. Hence we need <math>\sigma | where <math>Z </math> is a standard normal. Hence we need <math>\sigma \leq 0.001328</math>. | ||
Latest revision as of 21:02, 26 June 2024
Solution: B
We need to find [math]\sigma [/math] small enough so that the range of values outside [math]1.000 \pm .003[/math] cm has probability less than or equal to 1%. If [math]X[/math] has a normal distribution with mean 1 and standard deviation [math]\sigma [/math] then
[[math]]
P(X \in 1.000 \pm .003 ) = P(Z \in \pm 0.003/\sigma ) \geq 0.99 = P(Z \in \pm 2.576)
[[/math]]
where [math]Z [/math] is a standard normal. Hence we need [math]\sigma \leq 0.001328[/math].