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.
Accepted Solution
A:
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 %