At a factory that employs many workers, $30$% of the workers are members of the trade union $A$,

Question

At a factory that employs many workers, $30$% of the workers are members of the trade union $A$, $60$% are members of the trade union $B$, and $10$% are not members of any trade union. A sample of five workers is selected from the workers of the factory. Determine the mean and standard deviation for the number of workers in the sample who are members of $A$.[2] Find, correct to three significant figures, the probability that the sample contains not more than $2$ members of $A$.[2] Given that exactly $4$ workers in the sample are members of trade unions, find the probability that the majority of the workers in this sample are members of $A$.[4]

Accepted Answer

(a) mean = $1.5$, std. = $1.02$ (b) $0.837$ (c) $\frac{1}{9}$

Binomial Distribution - Binomial Distribution - General

Binomial Distribution - Binomial Distribution - General