Answer:
The Z-score for that day's temperature is 2.41, and since Z > 2, this temperature is significantly high.
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
If , the measure X is significantly high(Z > 2) or significantly low(Z < -2).
The mean high temperature on a particular day in January is 31 degrees F and the standard deviation is 8.7 degrees.
This means that
One year, the temperature was 52 degrees F on that day.
This means that .
What is the Z-score for that day's temperature?
The Z-score for that day's temperature is 2.41, and since Z > 2, this temperature is significantly high.
