Answer:
P(X<5)=0.0115
Step-by-step explanation:
-This is a binomial probability distribution problem expressed as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}[/tex]
-Given p=0.59, n=15, the probability that fewer than 5 people use their smartphones is calculated as follows:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X<5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)\\\\\\={15\choose 0}0.59^0(1-0.59)^{15}+{15\choose 1}0.59^1(1-0.59)^{14}+{15\choose 2}0.59^2(1-0.59)^{13}+{15\choose 3}0.59^3(1-0.59)^{12}+{15\choose 4}0.59^4(1-0.59)^{11}\\\\\\=0.0000+0.0000+0.0003+0.0021+0.0091\\\\=0.0115[/tex]
Hence, the probability of less than 5 people using their smartphones is 0.0115
