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.

The probability that the temperature on a given day in February is 22º or lower is 16.7 %

Step-by-step explanation:

Given:

Average Temperature,

Standard Deviation of Temperature, [tex\sigma=8.5^{\circ}[/tex]

We have to find: Probability that the temperature is 22° or lower

.i.e., P[ X ≤ 22 ]

Let X be the Temperature on a given day in February.

We use Z-score to calculate required probability.

First we convert X into Z using this relationship,

Now, Probability [ Z ≤ -0.965 ] = 0.167272 = 16.7 %

Therefore, The probability that the temperature on a given day in February is 22º or lower is 16.7 %

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