In a perfectly symmetrical distribution, the skewness is:a.Positiveb.Negativec.Zerod.Cannot be determined

Break Down the Problem

1. Identify the characteristics of a perfectly symmetrical distribution.
2. Determine the meaning of skewness.

Relevant Concepts

1. Symmetrical Distribution: In a perfectly symmetrical distribution, the left side of the distribution is a mirror image of the right side.
2. Skewness: Skewness measures the asymmetry of the distribution of values.
   • Positive skewness indicates a distribution with an asymmetrical tail extending toward the right.
   • Negative skewness indicates a distribution with an asymmetrical tail extending toward the left.
   • A skewness of zero indicates perfect symmetry.

Analysis and Detail

• For a perfectly symmetrical distribution, the mean, median, and mode are all equal, and the distribution balances out around the central point.
• This balance implies that there is no tail extending in either direction, which is represented mathematically by a skewness of zero.

Verify and Summarize

• Given the characteristics of a symmetrical distribution, the skewness is confirmed to be zero.

Final Answer

c. Zero