Respuesta :
Using the uniform distribution, it is found that:
a) The height of the density curve is of 0.25.
b) 31.25% of the time will the light flash more than 3.75 seconds after the subject clicks "Start".
c) The 38th percentile of this distribution is of 2.52 seconds. It means that 38% of the time, the light will go on in at most 2.52 seconds.
Uniform distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
In this problem, uniform between 1 and 5, hence [tex]a = 1, b = 5[/tex]
Item a:
The height of the uniform distribution is:
[tex]h = \frac{1}{b - a}[/tex]
Hence:
[tex]h = \frac{1}{5 - 1} = 0.25[/tex]
Item b:
[tex]P(X > 3.75) = \frac{5 - 3.75}{5 - 1} = 0.3125[/tex]
0.3125 x 100% = 31.25%
31.25% of the time will the light flash more than 3.75 seconds after the subject clicks "Start".
Item c:
The 38% percentile is x for which P(X < x) = 0.38, hence:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
[tex]0.38 = \frac{x - 1}{4}[/tex]
[tex]x - 1 = 4(0.38)[/tex]
[tex]x = 2.52[/tex]
The 38th percentile of this distribution is of 2.52 seconds. It means that 38% of the time, the light will go on in at most 2.52 seconds.
A similar problem is given at https://brainly.com/question/15855314
