Respuesta :
Using the normal distribution, it is found that the lengths for which a bolt will be destroyed are given by:
A. A bolt will be destroyed if the length is less than 11.8 cm or greater than 12.2 cm.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
[tex]\mu = 12, \sigma = 0.05[/tex]
The bounds within 4 standard deviations of the mean are [tex]Z = \pm 4[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-4 = \frac{X - 12}{0.05}[/tex]
X - 12 = -4 x 0.05
X = 11.8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]4 = \frac{X - 12}{0.05}[/tex]
X - 12 = 4 x 0.05
X = 12.2
Hence:
A. A bolt will be destroyed if the length is less than 11.8 cm or greater than 12.2 cm.
More can be learned about the normal distribution at https://brainly.com/question/4079902
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