Questions: If the heights of all adult females are normally distributed with a mean of 5.5 feet and a standard deviation of 1 foot, how tall is Jada if she is in the 82 nd percentile? Round your answer to one decimal place. Do not include units in your answer.

Solution Steps

To find Jada's height at the 82nd percentile, we first need to identify the z-score corresponding to this percentile. From the z-score table, we find that the closest probability to \(0.82\) is \(0.819\), which corresponds to a z-score of approximately \(Z = 0.92\).

We can calculate Jada's height using the formula for converting a z-score to a value in a normal distribution:

\[ X = \mu + Z \cdot \sigma \]

Where:

• \(X\) is the height we want to find,
• \(\mu = 5.5\) feet (mean height),
• \(Z = 0.92\) (z-score for the 82nd percentile),
• \(\sigma = 1\) foot (standard deviation).

Substituting the values into the formula:

\[ X = 5.5 + 0.92 \cdot 1 \]

Calculating this gives:

\[ X = 5.5 + 0.92 = 6.42 \]

Finally, we round Jada's height to one decimal place:

\[ X \approx 6.4 \]

Final Answer