Respuesta :
Answer: The required probability is 0.334.
Step-by-step explanation:
Since we have given that
N = 15 reservations
probability of reservations will not be used = 0.2
probability of reservations will be used = 1-0.2=0.8
Let X be the Binomial variable,that the number of reservations canceled.
We need to find the probability that more than 8 but less than 12 reservations.
So, it becomes,
[tex]P(8<X<12)=P(9)+P(10)+P(11)\\\\=^{15}C_9(0.8)^9(0.2)^6+^{15}C_{10}(0.8)^{10}(0.2)^5+^{15}C_{11}(0.8)^{11}(0.2)^4\\\\\approx 0.334[/tex]
Hence, the required probability is 0.334.
Answer:
Probability that more than 8 but less than 12 reservations will be used is 0.334 .
Step-by-step explanation:
We are given that a certain hotel chain finds 20% of the reservations will not be used which means that 20% of the reservations will be used.
Let X = number of reservations canceled
X ~ [tex]Binom(n=15,p = 0.80)[/tex]
The Probability distribution of Binomial distribution is given by;
[tex]P(X=r) = \binom{n}{r}p^{r}(1-p)^{n-r} ; x = 0,1,2,3,....[/tex]
where, n = number of trials(samples) taken = 15
r = number of success
p = probability of success i.e. success of reservations will be used
So, probability that more than 8 but less than 12 reservations will be used is given by = P(X = 9) + P(X = 10) + P(X = 11)
= [tex]\binom{15}{9}0.8^{9}(1-0.8)^{15-9} + \binom{15}{10}0.8^{10}(1-0.8)^{15-10} + \binom{15}{11}0.8^{11}(1-0.8)^{15-11}[/tex]
= [tex]5005*0.8^{9} *0.2^{6} + 3003*0.8^{10} *0.2^{5} + 1365*0.8^{11} *0.2^{4}[/tex]
= 0.043 + 0.103 + 0.188 = 0.334
Therefore, probability that more than 8 but less than 12 reservations will be used is 0.334 .
