Question

according to BLS 50% of all people will do volunteer work

a. probability that a random sample of 100 people would yield 40 volunteers at most

Answer 1

It is a binomial distribution problem with probability p = 50% = 50/100 = 0.50

total sample n = 100 and number of selection r = 40

Using binomial to normal approximation

mean = n *p = 100*0.5 = 50

standard deviation = sqrt{n*p*q}

where n = 100, p = 0.5 and q = 1- p = 1-0.5 = 0.5

this gives

standard deviation = sqrt{100*0.5*0.5}

= sqrt{25}

= 5

We have to find

setting the calculated values

(using excel function NORMSDIST(z), setting z = -2, we get NORMSDIST(-2) = 0.0228)

So, required probability is 0.0228