Multiple choice

What is the mean of the numbers 1,2,3, ..., 10 with frequencies 9C0, 9C1, 9C2 ,...., 9C9 respectively?

  1. 1.1 × 28

  2. 1.2 × 74

  3. 5.5

  4. 0.55
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C Correct answer
AI explanation

Using the binomial distribution properties, the mean of this data is calculated as the sum of x multiplied by 9Cx from x equals 0 to 9, all divided by the sum of 9Cx from x equals 0 to 9. The sum of x multiplied by 9Cx equals 9 multiplied by 2 to the power of 8, which is 2304, and the denominator is 2 to the power of 9, which is 512. Dividing 2304 by 512 yields a mean of 5.5, which is consistent with the expected value formula for a binomial distribution with n equal to 9 and p equal to 0.5.

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