Respuesta :
The probability that headway is within 1 standard deviation of the mean value is 0.890.
What is mean value?
By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.
The mean of a discrete probability distribution of a random variable X is equal to the sum over all possible values weighted by the likelihood of each value. To calculate the mean, one must multiply each potential value of X by its probability P(x), then add all of these products.
Given mean value is P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995).
The cdf for the distribution is
[tex]F(x)=\left \{ {{1 -\frac{1}{x^6} ,x > 1} \atop {0,x\le 1}} \right.[/tex]
Now calculate the value of F(1.445) and F(0.995).
F(1.445) = 1 - (1/(1.445)⁶)
F(0.995) = 0
Now putting the value of F(1.445) and F(0.995) in P( 0.995 ≤ x ≤ 1.445) = F(1.445) - F(0.995):
P( 0.995 ≤ x ≤ 1.445)
=1 - (1/(1.445)⁶) - 0
=0.890
To learn more about standard deviation, click on below link:
https://brainly.com/question/15059898
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