Step 1: Understanding the Question:
We are asked to pick the ISO standard from the 9000 family whose scope names five specific activities: design, development, processing, installation, and servicing.
Step 2: Key Formula or Approach:
Think of the old ISO 9000 family as three models of shrinking scope. The broadest model covers design through servicing. The middle model drops design and covers only production and installation. The narrowest model covers only final inspection and testing. ISO 9000 itself sits outside this list since it only gives definitions and principles rather than a certifiable scope.
Step 3: Detailed Explanation:
ISO 9000 is ruled out immediately since it is a vocabulary and principles document, not a scope of activities.
ISO 9003 is ruled out since its scope stops at final inspection and testing, well short of design or servicing.
ISO 9002 is ruled out since it stops at production and installation and specifically leaves out design and development, so it cannot be the standard the question describes.
ISO 9001 is the broadest model, and its stated scope is exactly design, development, production or processing, installation, and servicing, which is a direct match to every activity named in the question.
Step 4: Final Answer:
The standard covering design, development, processing, installation, and servicing together is ISO 9001. \[ \boxed{\text{ISO } 9001} \]