Question

It is known that about 65% of u.s. adults work during your summer vacation. Now consider a random sample of 80 u.s. adults what is the approximate probability that less than 60% of the samples adults will work during summer vacation

Answer 1

Say p be the probability that an adult work during the summer vacation, p = 0.65

We have a random sample of 80 U.S adults and we can approximate a binomial to normal approximation with the following statistics:

Mean = p = 0.65
Standard Deviation = √(pq/n) = √(0.65*0.35/80) =  0.053

Now, we need to find P(p < 0.60) = P( z < (0.60 - 0.65/0.053) ) = P(z < -0.94)

From the z-table, P(z < -0.94) = 0.1736

Hence, the probability that less than 60% of sampled adults will work during summer vacation is 0.1736.