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A random variable 'z' is less than or equal to one hundred ninety-three.

Mathematically, this is expressed as:

A. [tex]z \ \textless \ 193[/tex]
B. [tex]z \ \textgreater \ 193[/tex]
C. [tex]z \geq 193[/tex]
D. [tex]z \leq 193[/tex]

Answer :

To solve this question, we need to translate the statement "A random variable 'z' is less than or equal to one hundred ninety-three" into a mathematical inequality.

1. Identify the keyword: The phrase "less than or equal to" gives us a clue about the type of inequality we are dealing with.

2. Choose the correct inequality symbol:
- "Less than" alone would use the symbol `<`.
- "Equal to" would use the symbol `=`.
- "Less than or equal to" combines these ideas and uses the symbol `≤`.

3. Match it to the problem: We are given that z must be less than or equal to 193. So, the correct mathematical expression using the appropriate symbol is:

[tex]\[
z \leq 193
\][/tex]

4. Select the correct answer option: Based on this expression, we look through the given answer choices:
- [tex]$z < 193$[/tex]
- [tex]$z > 193$[/tex]
- [tex]$z \geq 193$[/tex]
- [tex]$z \leq 193$[/tex]

The correct choice is [tex]$z \leq 193$[/tex] because it directly matches the expression derived from the given statement.

Therefore, the statement "A random variable 'z' is less than or equal to one hundred ninety-three" is mathematically expressed as [tex]\( z \leq 193 \)[/tex].

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