Respuesta :
Answer:
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, [tex]\mu=30.2^{\circ}[/tex]
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,
[tex]Z=\frac{X-\mu}{\sigma}=\frac{22-30.2}{8.5}=-0.965[/tex]
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 %
The probability that the temperature on a given day in February is 22º or lower is 0.1672 or 16.72% if the daytime high temperatures in New York in February are normally distributed with an average of 30.2º and a standard deviation of 8.5º
What is the standard deviation?
It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
We have:
Daytime high temperatures in New York in February are normally distributed.
The average temperature
[tex]\rm \mu= 30.2\°[/tex]
Standard deviation
[tex]\sigma= 8.5 \°[/tex]
X = 22°
We know the formula for the Z test:
[tex]\rm Z = \frac{X - \mu}{\sigma}[/tex]
[tex]\rm Z = \frac{22-30.2}{8.5}[/tex]
Z = -0.9647 ≈ 0.965
Now the probability that the temperature on a given day in February is 22º or lower.
P(X<22º) = 0.1672 or 16.72% (from the Z-table)
Thus, the probability that the temperature on a given day in February is 22º or lower is 0.1672 or 16.72% if the daytime high temperatures in New York in February are normally distributed with an average of 30.2º and a standard deviation of 8.5º
Learn more about the standard deviation here:
brainly.com/question/12402189
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