Respuesta :
Answer:
A reading of 1.25ºC separates the highest 13% of the thermometers from the rest.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0.0°C and a standard deviation of 1.0°C. This means that [tex]\mu = 0, \sigma = 1[/tex].
What readings separates the highest 13% of the thermometers from the rest?
This is the value of X when Z has a pvalue of 0.87.
This is [tex]Z = 1.25[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.25 = \frac{X - 0}{1}[/tex]
[tex]X = 1.25[/tex]
A reading of 1.25ºC separates the highest 13% of the thermometers from the rest.
