Question

The probability that an individual is​ left-handed is 0.170. In a class of 46 ​students, what is the probability of finding five​ left-handers? Round the answer to the nearest thousandth.

Answer 1

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:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{46}{k} 0.17^{k} 0.83^{46-k}$

Then, the probability of finding five​ left-handers in the sample is:

$P(x=5) = \dbinom{46}{5} 0.17^{5}\cdot 0.83^{41}=1370754*0.000142*0.000481=0.094$