Question

Binomial – 70% of teenagers text only messages.  In a random sample of 10 teenagers what is the probability that 5 only text.

Multiple choice:

a) .5

b) .7

c) .103

Answer 1

Formulas: 1) Binomial distribution : P(X = x) = * p* * (1 - p)-* Where n = total number of trials x = number of success's we chosen out of n p = probability of success. 2) () n! x!#(n-x)! Let X = number of teenagers texts out of 10. Now we have The number of teenagers selected=n= 10. 70% of teenagers text only messages. =The probability that a randomly selected teenager text is p = 70% = 0.7. X follows binomial distribution with n = 10 and p = 0.7.

Now we have to find P(X = 5). P(X = 5) = (13) * (0.7)5 * (1 – 0.7)10-5 *(0.7)5 * 0.35 5!-(10-5)! 10! 10! 5!-(5)! (0.7)5 * (0.3)5 = 252 * (0.7)5 * (0.3) = 0.103 .. P(X = 5) = 0.103

answer = 0.103