Answer:
The temperature for P 84 is approximately 1ºC.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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 degrees and standard deviation of 1.00°C. This means that and
This is the temperature reading separating the bottom 84 % from the top 16 %.
This temperature is the value of X when Z has a pvalue of 0.84. This happens at .
So
The temperature for P 84 is approximately 1ºC.