Question

Suppose that past history shows that 60% of college students prefer brand c cola. a sample of 5 students is to be selected. based on the binomial probability distribution, the probability that less than 2 prefer brand c is ________.

Answer 1

The probability is 8.7%.

To find P(X<2), we find P(X = 1 or X = 0). For a binomial distribution, we use the formula

`_nC_r(p)^r(1-p)^(n-r)`

For this problem, p=0.6 and n=5:

`_5C_1(0.6)^1(1-0.6)^4+_5C_0(0.6)^0(1-0.6)^5 \\ \\_5C_1(0.6)(0.4)^4+_5C_0(0.4)^5 \\ \\ (5!)/(1!4!)(0.6)(0.4)^4+(5!)/(0!5!)(0.4)^5 \\ \\ 5(0.6)(0.4)^4+(0.4)^5 \\ \\0.0768+0.01024 = 0.08704\approx0.087=8.7%`