Questions: The deciles of any distribution are the points that mark off the highest and lowest 10% of the observations. How many standard deviations on either side of the mean do the deciles in a normal distribution lie? Hint: Look for a center value of 0.8015.

Solution Steps

To find how many standard deviations on either side of the mean the deciles lie in a normal distribution, we need to determine the z-scores that correspond to the 10th and 90th percentiles. These z-scores represent the number of standard deviations away from the mean. We can use a statistical library in Python to find these z-scores.

To find the deciles in a normal distribution, we calculate the z-scores corresponding to the 10th and 90th percentiles. The results are: \[ z_{10th} = -1.2816 \quad \text{and} \quad z_{90th} = 1.2816 \]

The z-scores indicate how many standard deviations the deciles are from the mean. Specifically:

• The 10th percentile is located at \( -1.2816 \) standard deviations below the mean.
• The 90th percentile is located at \( 1.2816 \) standard deviations above the mean.

Final Answer