Question

This lest. 11 pis posso This Question: 1 pt 9 of 11 complete) O Assume that when adults with the readonly selected, 67% we them in meeting or dos 11 wut smartphone tere randomly selected find the probability that fewer thand of the use their smartphones in meetings or dames The probability is (Type en tager or decimal rounded to four decimal places as needed)

Answer 1

p = 47%

n = 11

Binomila Probability formula:

P(X = x) = n! / x!(n-x)! *px * (1-p)n-x

Complement rule:

P(not A) =1 - P(A)

The binomial probability x = 0,1,2,3 (Fewer than 4)

P(x = 0) = 11! / 0!(11-0)!*0.47^0*(1-0.47)^(11-0)

P(x = 0) = 1*0.47^0*0.53^11 = 0.0009

P(x = 1) = 11! / 1!(11-1)!*0.47^1*(1-0.47)^(11-1)

P(x = 1) = 11*0.47^1*0.53^10 = 0.0090

P(x = 2) = 11! / 2!(11-2)!*0.47^2*(1-0.47)^(11-2)

P(x = 2) = 55*0.47^2*0.53^9 = 0.0401

P(x = 3) = 11! / 3!(11-3)!*0.47^3*(1-0.47)^(11-3)

P(x = 3) = 165*0.47^3*0.53^8 = 0.1067

Use the additional rule of disjoint events:

P(X < 4) = P(x = 0)+P(x = 1)+P(X = 2)+P(X = 3)

P(X < 4) = 0.0009+0.0090+0.0401+0.1067 = 0.1567

Answer : 0.1567