Respuesta :
Answer:
0.8571,0.6667
Step-by-step explanation:
Given that the time it takes a nine-year old to eat a donut
is between 0.5 and 4 minutes,inclusive.
Let X = the time,
in minutes, it takes a nine-year old child to eat a donut.
Then X: U (0.5, 4).
The probability distribution function of X would be
[tex]P(X) = \frac{1}{4-0.5} =0.2857[/tex]
Cumulative function CDF would be
[tex]F(x) = \frac{x-0.5}{3.5}[/tex]
a) The probability that a randomly selected nine-year old
child eats a donut in at least two minutes is
=[tex]P(X\geq 2) = 1-F(2)\\= 1-\frac{2-0.5}{3.5} \\=0.8571[/tex]
b) the probability that a different nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes.
=[tex]P(X>2/x>1.5) = \frac{P(X>2)}{P(X>1,5)} \\= \frac{1-\frac{2-0.5}{3.5} }{1-\frac{1.5-0.5}{3.5} } \\=\frac{0.571429}{0.857143} \\=0.6667[/tex]
