Answer:
The probability of finding five left-handers in the sample is P(x=5)=0.094.
Step-by-step explanation:
We can model this variable with a binomial distribution, with parameters n=46 (sample size) and p=0.170 (the probability that an individual is left-handed).
The probability that k individuals are left-handed in the sample can be calculated as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{46}{k} 0.17^{k} 0.83^{46-k}\\\\\\[/tex]
Then, the probability of finding five left-handers in the sample is:
[tex]P(x=5) = \dbinom{46}{5} 0.17^{5}\cdot 0.83^{41}=1370754*0.000142*0.000481=0.094\\\\\\[/tex]
