Question

The average high temperature in orlando in november is 78°. suppose that the temperatures are normally distributed, and the standard deviation is 3°. what temperature represents the 30th percentile?

Answer 1

The temperature representing the 30th percentile for Orlando's November high temperatures is approximately 76.44°F, calculated using a z-score of -0.52 and the given mean (78°F) and standard deviation (3°F).

Step-by-step explanation:

The question relates to finding the 30th percentile of normally distributed temperatures in Orlando in November. With an average high temperature of 78°F and a standard deviation of 3°F, we can use the normal distribution and z-scores to calculate this.

To calculate the 30th percentile, we can use the z-score associated with the 30th percentile in the standard normal distribution. This score tells us how many standard deviations away from the mean our value lies. We look up the z-score for the 30th percentile, which is approximately -0.52.

Now we apply the formula for finding the actual temperature value: X = μ + z⋅σ. Here, X is the temperature we're looking for, μ is the mean temperature (78°F), z is the z-score (-0.52), and σ is the standard deviation (3°F).

Step-by-step calculation:

1. Identify the z-score for the 30th percentile: Approximately -0.52.
2. Apply the formula: X = 78 + (-0.52 ⋅ 3).
3. Calculate the result: X = 78 - 1.56.
4. X = 76.44°F.

Thus, the temperature representing the 30th percentile for high temperatures in Orlando in November is approximately 76.44°F.