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Answer :
Final answer:
The summer high temperature that is the 84th percentile of this distribution is approximately 98.31.
Explanation:
To find the summer high temperature that is the 84th percentile of this distribution, we need to calculate the corresponding z-score and then convert it back to the actual temperature value.
- First, we calculate the z-score using the formula:
z = (x - mean) / standard deviation - Substituting the given values:
z = (x - 95.1) / 3.1 - Next, we need to find the z-score corresponding to the 84th percentile. Since the normal distribution is symmetric, we can use the standard normal distribution table or a calculator to find the z-score that corresponds to the area to the left of the 84th percentile, which is 0.84.
- Looking up the z-score in the standard normal distribution table, we find that the z-score is approximately 1.04.
- Now, we can solve for the temperature value:
1.04 = (x - 95.1) / 3.1 - Multiplying both sides by 3.1:
3.214 = x - 95.1 - Adding 95.1 to both sides:
x = 98.314
Therefore, the summer high temperature that is the 84th percentile of this distribution is approximately 98.31.
Learn more about calculating percentiles in a normal distribution here:
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