Question

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees and standard deviation of 1.00°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 84​, the 84 th percentile. This is the temperature reading separating the bottom 84 % from the top 16 %. The temperature for P 84 is approximately_________?

Answer 1

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 $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 $\mu = 0$ and $\sigma = 1$

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 $Z = 1$.

So

$Z = \frac{X - \mu}{\sigma}$

$1 = \frac{X - 0}{1}$

$X = 1$

The temperature for P 84 is approximately 1ºC.