GATE XE (Engineering Sciences) 2016 - Question 11

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Section: Engineering Mathematics | Marks: 1

A company records heights of all employees. Let X and Y denote the errors in the average height of male and female employees respectively. Assume that 𝑋𝑋 ~ 𝑁𝑁(0, 4) and π‘Œπ‘Œ ~ 𝑁𝑁(0, 9) and they are independent. Then the distribution of 𝑍𝑍= (𝑋𝑋+ π‘Œπ‘Œ)/2 is

  • A. 𝑁𝑁(0, 6.5)
  • B. 𝑁𝑁(0, 3.25)
  • C. 𝑁𝑁(0, 2)
  • D. 𝑁𝑁(0, 1)

Answer: B. 𝑁𝑁(0, 3.25)

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