Final answer:
To find the 30th percentile temperature for Orlando in November using a normal distribution with a mean of 78° and a standard deviation of 3°, we calculate a z-score of -0.52, which results in a temperature of 76.44°. After rounding to the nearest whole number, the final answer is 76°, representing the 30th percentile.
Step-by-step explanation:
To find the 30th percentile of the normally distributed temperatures in Orlando for November, we use the average high temperature (mean) of 78° and a standard deviation of 3°. Percentiles in a normal distribution can be determined by using a z-score table or a percentile calculator. The z-score that corresponds to the 30th percentile is approximately -0.52. Applying the z-score formula:
Z = (X - μ) / σ
Where Z is the z-score, X is the value on the normal distribution, μ is the mean, and σ is the standard deviation:
-0.52 = (X - 78) / 3
Solving for X gives us:
X = -0.52 * 3 + 78 = 76.44°
Since temperature is commonly rounded to the nearest whole number, the closest answer to 76.44° would be 76°, making option 2 the correct choice.
Thus, the final answer is 76°, which represents the 30th percentile of high temperatures in Orlando in November.