Questions: A normal population has a mean of 55 and a standard deviation of 9. What is the 84th percentile of the population? Use the π-84 Plus calculator. Round the answer to at least one decimal place.

Solution Steps

We are given a normal population with the following parameters:

• Mean ($\mu$): 55
• Standard Deviation ($\sigma$): 9

The z-score corresponding to the 84th percentile is approximately $Z = 1.0$.

Using the formula for the percentile value in a normal distribution:

$$X = \mu + Z \cdot \sigma$$

Substituting the known values:

$$X = 55 + 1.0 \cdot 9$$

Calculating this gives:

$$X = 55 + 9 = 64$$

The 84th percentile value is rounded to one decimal place, which is:

$$X = 64.0$$

Final Answer