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The random variable X has a uniform distribution with values between 10 and 14.

What is the mean and standard deviation of X?
(Round your answer to three decimal places.)

User Rcravens
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1 Answer

6 votes

Answer:

1.155

Explanation:

The mean of a uniform distribution is defined as the average of the lower and upper bounds of the distribution. The standard deviation of a uniform distribution is defined as the square root of the variance, which is equal to the square of the range of the distribution divided by 12.

In this case, the lower bound of the distribution is 10 and the upper bound is 14, so the mean of the distribution is (10 + 14)/2 = 12.

The range of the distribution is 14 - 10 = 4, so the variance is (4^2)/12 = 16/12 = 4/3. The standard deviation is the square root of this value, which is approximately 1.155. Rounded to three decimal places, the standard deviation is 1.155.

Therefore, the mean of the random variable X is 12 and the standard deviation is 1.155.

User JelleP
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