Multiple choice

he mean and standard deviation of a normal distribution are 50 and 10 respectively. What percentage of observations lie between 30 and 70 (approx)?

  1. 35%

  2. 95%

  3. 82%

  4. 99.7%
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B Correct answer
Explanation

The interval from 30 to 70 is 20 units on either side of the mean 50. Since the standard deviation is 10, this interval is within 2 standard deviations of the mean. Approximately 95% of observations lie within 2 standard deviations in a normal distribution.

AI explanation

For a normal distribution, the empirical rule states that approximately 95% of observations lie within two standard deviations of the mean. Here, two standard deviations equal 2 multiplied by 10, which is 20. Adding and subtracting 20 from the mean of 50 gives the exact interval from 30 to 70. Therefore, the percentage of observations in this range is 95%.

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