Answer :
Answer:
a) 0.3889
b) 0.5
c) 0.8333
d) The mean is 250 and the standard deviation is 51.96.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability of finding a value of X higher than x is:
[tex]P(X > x) = 1 - \frac{x - a}{b-a}[/tex]
The probability of finding a value of X between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The mean and the standard deviation are, respectively:
[tex]M = \frac{a+b}{2}[/tex]
[tex]S = \sqrt{\frac{b-a}^{2}{12}}[/tex]
A random variable follows the continuous uniform distribution between 160 and 340.
This means that [tex]a = 160, b = 340[/tex]
a)
[tex]P(220 \leq X \leq 290) = \frac{290 - 220}{340 - 160} = 0.3889[/tex]
b)
[tex]P(160 \leq X \leq 250) = \frac{250 - 160}{340 - 160} = 0.5[/tex]
c)
[tex]P(X > 190) = 1 - \frac{190 - 160}{340 - 160} = 0.8333[/tex]
d)
[tex]M = \frac{160 + 340}{2} = 250[/tex]
[tex]S = \sqrt{\frac{340 - 160}^{2}{12}} = 51.96[/tex]
The mean is 250 and the standard deviation is 51.96.