Answer :
The probability is approximately 0.7967.
The percentage of days with a high temperature between 66 and 80 degrees Fahrenheit, hence correct answer is 72.99%.
To find the percentage of days with a high temperature between 66 and 80 degrees Fahrenheit, we need to use the z-table and the properties of the normal distribution.
The z-score is a measure of how many standard deviations a data point is from the mean. It is calculated using the formula:
z = (X - μ) / σ
where:
X = the value (temperature in this case)
μ = the mean (75 degrees Fahrenheit)
σ = the standard deviation (6 degrees Fahrenheit)
Now, let's calculate the z-scores for both temperatures:
For X = 66 degrees Fahrenheit:
z1 = (66 - 75) / 6 = -1.5
For X = 80 degrees Fahrenheit:
z2 = (80 - 75) / 6 = 0.83 (rounded to two decimal places)
Now, we need to find the area under the normal curve between these two z-scores. We can use the standard normal distribution table (z-table) to find the probabilities corresponding to these z-scores.
Looking up the z-table for -1.5, we find that the probability is approximately 0.0668.
Looking up the z-table for 0.83, we find that the probability is approximately 0.7967.
Now, we need to find the percentage of days between these two temperatures. Since the temperatures are normally distributed, this percentage is the difference between the probabilities we just found:
Percentage = (0.7967 - 0.0668) * 100 ≈ 0.7299 * 100 ≈ 72.99%
So, the correct answer is 72.99%.
Learn more about normal distribution here:
https://brainly.com/question/15103234
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