Question

Assume that the readings on the thermometers are normally idistributed with a mean of 0◦ and a standard deviation of 1.00◦C. Find P25, the 25th percentile. This is the temperature reading separating the bottom 25 % from the top 75 %

Answer 1

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 $\mu$ 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◦ and a standard deviation of 1.00◦C. This means that $\mu = 0, \sigma = 1$

Find P25, the 25th percentile.

This is the value of X when Z has a pvalue of 0.25. So we use $Z = -0.675$, since this happens between $Z = -0.67$ and $Z = -0.68$.

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

$-0.675 = \frac{X - 0}{1}$

$X = -0.675$

This temperature reading is -0.675ºC.