Daytime high temperatures in New York in February are normally distributed with an average of 30.2º and a standard deviation of 8.5º.
Estimate the probability that the temperature on a given day in February is 22º or lower.
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To estimate the probability that the temperature on a given day in February is 22º or lower, we can use the standard normal distribution.
First, we need to standardize the value of 22º using the z-score formula:
Z = (X - μ) / σ
where:
Z is the z-score,
X is the value we want to standardize (22º in this case),
μ is the mean of the distribution (30.2º),
σ is the standard deviation of the distribution (8.5º).
Thus, the z-score is:
Z = (22 - 30.2) / 8.5
Calculating this, we get:
Z = -0.9647
Next, we need to look up the area under the standard normal distribution curve to the left of this z-score. This area represents the probability that a randomly selected temperature is 22º or lower.
Using a standard normal distribution table or calculator, we find that the area to the left of -0.9647 is approximately 0.1659.
Therefore, the estimated probability that the temperature on a given day in February is 22º or lower is about 0.1659, or 16.59%.
enter your data into
http://davidmlane.com/hyperstat/z_table.html
to get .8327