Question

It is estimated that 6000 of the 10000 voting residents of a town are against a new sales tax. If 14 eligible voters are selected at random and asked their​ opinion, what is the probability that at most 8 favor the new​ tax?

Answer 1

Here we are given that 6000 out of 10000 are against the new sales tax.

Therefore the proportion of voting residents who are against the new sales tax

the proportion of voting residents who are in favor of new sales tax

Therefore the number of successes out of n people follows a binomial distribution and the pmf is given by:

  

Therefore the probability that at most 8 out 14 favors the new sales tax is obtained from binomial distribution.

Here, we nave n=14, p=0.4, q=(1-p)=0.6.

At most 8 implies that the number of successes out of 14 is at most 8 ie less than or equal to 8.

ie

This is also equivalent to

the probability that at most 8 favor the new​ tax=0.9417