Assume that the readings on the thermometers are normally idistributed with a mean of 0◦ and a standard deviation of 1.00◦C. Fin

Question

mario62

2 months ago

12

Assume that the readings on the thermometers are normally idistributed with a mean of 0◦ and a standard deviation of 1.00◦C. Fin

d P25, the 25th percentile. This is the temperature reading separating the bottom 25 % from the top 75 %

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-03-24T23:33:10+03:00

Answer:

The recorded temperature is -0.675ºC.

Detailed explanation:

To tackle problems involving normally distributed samples, the z-score formula can be utilized.

In a distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score for a specific measure X is calculated as follows:

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

The Z-score indicates how many standard deviations a given measure deviates from the mean. Once the Z-score is determined, we refer to the z-score table to obtain the corresponding p-value. This p-value represents the likelihood that the measure's value is less than X, thereby indicating the percentile of X. By taking 1 minus the p-value, we find the probability that the measure's value exceeds X.

For this scenario, we know that:

Assuming the thermometer readings follow a normal distribution with a mean of 0◦ and a standard deviation of 1.00◦C, this leads us to $\mu = 0, \sigma = 1$

We need to determine P25, which is the 25th percentile.

This represents the value of X corresponding to Z with a p-value of 0.25, thus we utilize $Z = -0.675$ , applicable between $Z = -0.67$ and $Z = -0.68$ .

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

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

$X = -0.675$

The recorded temperature is -0.675ºC.