Final answer:
To find the 9th percentile (P9) for a normal distribution with a mean of 0°C and a standard deviation of 1.00°C, we look for the z-score corresponding to the 9th percentile, which is approximately -1.34, and then use the formula X = Z × σ + μ to calculate P9 as -1.34°C.
Step-by-step explanation:
To find P9, the 9th-percentile of a normally distributed set of thermometer readings with a mean (average) of 0°C and a standard deviation of 1.00°C, we need to determine the temperature reading that separates the bottom 9% from the top 91%.
First, we find the z-score that corresponds to the 9th percentile of the standard normal distribution. This z-score represents the number of standard deviations below the mean.
Looking up the 9th percentile in the z-table, we find the z-score associated with P9, which is approximately -1.34.
Once the z-score has been identified, we use the z-score formula:
Z = (X - μ) / σ
We rearrange the formula to solve for X, which represents P9:
X = Z × σ + μ
Substituting our values, we get:
X = (-1.34 × 1.00°C) + 0°C = -1.34°C
The temperature reading that corresponds to P9 is -1.34°C.