5. During a blood collection, a sample of 100 people is chosen from the population of a French city. This population is large enough to assimilate this choice to sampling with replacement. We denote by $X$ the random variable that associates to each sample of 100 people the number of universal donors in that sample. a. Justify that $X$ follows a binomial distribution and specify its parameters. b. Determine to $10 ^ { - 3 }$ near the probability that there are at most 7 universal donors in this sample. c. Show that the expectation $E ( X )$ of the random variable $X$ is equal to 7.14 and that its variance $V ( X )$ is equal to 6.63 to $10 ^ { - 2 }$ near.
The required probability is $P _ { S } ( B )$. By definition, we have:
5. During a blood collection, a sample of 100 people is chosen from the population of a French city. This population is large enough to assimilate this choice to sampling with replacement.\\
We denote by $X$ the random variable that associates to each sample of 100 people the number of universal donors in that sample.\\
a. Justify that $X$ follows a binomial distribution and specify its parameters.\\
b. Determine to $10 ^ { - 3 }$ near the probability that there are at most 7 universal donors in this sample.\\
c. Show that the expectation $E ( X )$ of the random variable $X$ is equal to 7.14 and that its variance $V ( X )$ is equal to 6.63 to $10 ^ { - 2 }$ near.\\