Average of prime numbers: Find the average of all prime numbers between 60 and 90.

Difficulty: Medium

Correct Answer: 74.7

Explanation:

Introduction / Context:The task is to list primes in the interval and compute their arithmetic mean. This checks prime identification and mean calculation skills.Given Data / Assumptions:

  • Interval: 60 to 90 inclusive of endpoints only if prime

Concept / Approach:Enumerate primes, sum them, divide by count.Step-by-Step Solution:

Primes in (60, 90): 61, 67, 71, 73, 79, 83, 89Sum = 61 + 67 + 71 + 73 + 79 + 83 + 89 = 523Count = 7Average = 523 / 7 = 74.7142857, which rounds to 74.7

Verification / Alternative check:Cross check primality quickly: none of the numbers are divisible by 2, 3, 5, 7 except as expected for composites; list is correct.Why Other Options Are Wrong:

  • 72, 74, 73.6: Do not equal the computed mean. 74.7 is the correct rounded value.

Common Pitfalls:Missing a prime like 83 or including a composite such as 77 or 87 by mistake.Final Answer:

74.7

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