Answer:
This temperature reading is -0.675ºC.
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 on the thermometers are normally distributed with a mean of 0◦ and a standard deviation of 1.00◦C. This means that [tex]\mu = 0, \sigma = 1[/tex]
Find P25, the 25th percentile.
This is the value of X when Z has a pvalue of 0.25. So we use [tex]Z = -0.675[/tex], since this happens between [tex]Z = -0.67[/tex] and [tex]Z = -0.68[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 0}{1}[/tex]
[tex]X = -0.675[/tex]
This temperature reading is -0.675ºC.
The temperature reading separating the bottom 25% from the top 75% is -0.68°C
Z score is used to determine by how many standard deviations the raw score is above or below the mean.
It is given by:
z = (raw score - mean) / standard deviation
The 25th percentile has a z score of -0.68
Hence:
-0.68 = (x - 0)/1
x = -0.68
The temperature reading separating the bottom 25% from the top 75% is -0.68°C
Find out more on z score at: https://brainly.com/question/25638875
