Respuesta :
Answer:
a) P(x=5) = 0.2456
b) P(x≥6) = 0.3526
c) P(x<4) = 0.1887
Step-by-step explanation:
We can model this as a binomial experiment, with sample size n=10 and p=0.49.
To calculate the probability of having k subjects with very little confidence in the sample of 10, we solve:
[tex]P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}[/tex]
a) We have to calculate P(x=5).
For a binomial variable with n=10 and p=0.49, this can be calculated as:
[tex]P(x=5) = \dbinom{10}{5} p^{5}q^{5}=252*0.0282*0.0345=0.2456\\\\[/tex]
b) We have to calculate P(x≥6). This can be calculated as:
[tex]P(x\geq6)=P(x=6)+P(x=7)+P(x=8)+P(x=9)+P(x=10)\\\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0138*0.0677=0.1966\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.0068*0.1327=0.1080\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0033*0.2601=0.0389\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0016*0.51=0.0083\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.0008*1=0.0008\\\\\\P(x\geq6)=0.1966+0.1080+0.0389+0.0083+0.0008\\\\P(x\geq6)=0.3526[/tex]
c) We have to calculate P(x<4). That is:
[tex]P(x<4)=P(x=0)+P(x=1)+P(x=2)+P(x=3)\\\\\\P(x=0) = \binom{10}{0} p^{0}q^{10}=1*1*0.0012=0.0012\\\\P(x=1) = \binom{10}{1} p^{1}q^{9}=10*0.49*0.0023=0.0114\\\\P(x=2) = \binom{10}{2} p^{2}q^{8}=45*0.2401*0.0046=0.0494\\\\P(x=3) = \binom{10}{3} p^{3}q^{7}=120*0.1176*0.009=0.1267\\\\\\P(x<4)=0.0012+0.0114+0.0494+0.1267\\\\P(x<4)=0.1887[/tex]
