High School

Summer high temperatures are distributed normally with a mean of 95.1 and a standard deviation of 3.1.

Note: Round your z-score to 2 decimal places before calculating a probability.

What is the summer high temperature that is the 84th percentile of this distribution?

A. 92.5
B. 92
C. 98.2
D. 97.7
E. None of the above

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.

  1. First, we calculate the z-score using the formula:
    z = (x - mean) / standard deviation
  2. Substituting the given values:
    z = (x - 95.1) / 3.1
  3. 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.
  4. Looking up the z-score in the standard normal distribution table, we find that the z-score is approximately 1.04.
  5. Now, we can solve for the temperature value:
    1.04 = (x - 95.1) / 3.1
  6. Multiplying both sides by 3.1:
    3.214 = x - 95.1
  7. 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:

https://brainly.com/question/31035366

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