Respuesta :
Answer:
a) [tex]n = 50, p = \frac{1}{6}[/tex]
b) [tex]n = 16, p = \frac{1}{100}[/tex]
c) [tex]n = 26, p = 0.25, \mu = 6.5[/tex]
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And [tex]p[/tex] is the probability of X happening.
(a) A fair die is rolled 50 times. X = number of times a 5 is rolled
The die is rolled 50 times, so [tex]n = 50[/tex].
Each roll can have 6 outcomes. So the probability that 5 is rolled is [tex]p = \frac{1}{6}[/tex]
(b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win.
You buy 16 boxes of cereal, so [tex]n = 16[/tex].
1 of 100 are winners. So [tex]p = \frac{1}{100}[/tex].
(c) Jack likes to play computer solitaire and wins about 25% of the time. X = number of games he wins out of his next 26 games.
He plays 26 games, so [tex]n = 26[/tex].
He wins 25% of the time, so [tex]p = 0.25[/tex]
We have that [tex]\mu = np[/tex]. So [tex]\mu = 26*0.25 = 6.5[/tex]
