Answer :
There is around a 79.17% chance that the city will have a temperature lower than 82.5 degrees. we first need to calculate the Z-score. The Z-score is a measure of how many standard deviations an element is from the mean.
We calculate the Z-score with the following formula:
Z = (X - μ) / σ
where:
- X is the element (in this case, the threshold temperature of 82.5 degrees),
- μ is the mean temperature (in this case, 76 degrees), and
- σ is the standard deviation (in this case, 8 degrees).
Plugging the values into the formula we get: Z = (82.5 - 76) / 8 = 0.8125 This means that a temperature of 82.5 degrees is 0.8125 standard deviations above the mean temperature. We now use the cumulative distribution function (CDF), which calculates the probability that a random variable is less than or equal to a certain value. Using the normal distribution's CDF with our Z score of 0.8125, we find that the probability of the city having a temperature lower than 82.5 degrees is approximately 0.7917, or 79.17%.
To know more about standard deviations visit :-
https://brainly.com/question/13336998
#SPJ11
