Assume that when adults with smartphones are randomly selected, 57% use them in meetings or classes. If 9 adult smartphone users are randomly selected, find the probability that at least 3 of them use their smartphones in meetings or classes The probability is ?
Accepted Solution
A:
Answer: 0.9617Step-by-step explanation:Given : The proportion of adults use their phones in meetings or classes : p=0.57Number of adults randomly selected : n= 9Let x be the random variable that represents the number of adults use their phones in meetings or classes.By using binomial probability formula, to find the probability of getting success in x trials.[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]The probability that at least 3 of them use their smartphones in meetings or classes will be :-[tex]P(x\geq3)=1-P(x<3)\\\\=1-(P(0)+P(1)+P(2))\\\\=1-(^9C_0(0.57)^0(0.43)^9+^9C_1(0.57)^1(0.43)^8)\\\\=1-((0.43)^9+(9)(0.57)^1(0.43)^8+(36)(0.57)^2(0.43)^7)\\\\=0.961708368616\approx0.9617[/tex]Hence, the required probability is 0.9617 .