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 and standard deviation
, the z-score for a specific measure X is calculated as follows:
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
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 , applicable between
and
.
The recorded temperature is -0.675ºC.