Respuesta :
Using the normal distribution, it is found that the two readings that are cutoff values separating the rejected thermometers from the others are -1.96ºC and 1.96ºC.
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 = 0, \sigma = 1[/tex].
The z-score that cuts off the bottom and top 2.5% of the distribution is [tex]z = \pm 1.96[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 0}{1}[/tex]
X = -1.96
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 0}{1}[/tex]
X = 1.96
The two readings that are cutoff values separating the rejected thermometers from the others are -1.96ºC and 1.96ºC.
More can be learned about the normal distribution at https://brainly.com/question/27879230
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