MATH SOLVE

2 months ago

Q:
# Thermometer Error. 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. What readings separates the highest 13% of the thermometers from the rest? (Round answer to two decimal places)

Accepted Solution

A:

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.