A random variable X is best described by a continuous uniform distribution from 20 to 45 inclusive. The standard deviation of this distribution is approximately
Use rule of thumb for SD from range. The standard deviation is approximately one-fourth the range.
6.25
To find the standard deviation of a continuous uniform distribution, we can use the formula:
Standard deviation = (b - a) / √12
where 'a' is the lower bound of the distribution and 'b' is the upper bound.
In this case, the lower bound 'a' is 20 and the upper bound 'b' is 45.
So, the standard deviation is approximately:
Standard deviation = (45 - 20) / √12
Standard deviation ≈ 25 / √12
Standard deviation ≈ 7.21 (rounded to two decimal places)
Therefore, the standard deviation of this continuous uniform distribution is approximately 7.21.
To find the standard deviation of a continuous uniform distribution, you can use the formula:
Standard Deviation = (b - a) / √12
where "a" is the lower bound of the distribution and "b" is the upper bound. In this case, a = 20 and b = 45.
Substituting the values into the formula:
Standard Deviation = (45 - 20) / √12
= 25 / √12
≈ 7.21
Therefore, the standard deviation of the continuous uniform distribution is approximately 7.21.