Assume that when adults with smartphones are randomly selected, 52% use them in meetings or classes. If 10 adult smartphone users are randomly selected, find the probability that fewer than 5 of them use their smartphones in meetings or classes.

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Assume that when adults with smartphones are randomly​ selected, 52​% use them in meetings or classes. If 10 adult smartphone users are randomly​ selected, find the probability that fewer than 5 of them use their smartphones in meetings or classes.

nick1337 · Accepted Answer

Step 1 Given Information: 52% of adults use their smartphones in meetings or classes. i.e., p=0.52 If n=10 adult smartphone users are randomly selected, to find the probability that fewer than 5 of them use their smartphones in meetings or classes: Let X denote the number of smartphone users who use their smartphones in meetings or classes and X follows Binomial distribution with number of trials n=10 and probability of success p=0.52. Probability mass function of Binomial variable is given by the formula: P(X=x)=nCxpx(1−p)n−x Step 2 Required probability is obtained as follows: P(X&amp;lt;5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4) =10C0(0.52)0(1−0.52)10−0+10C1(0.52)1(1−0.52)10−1+10C2(0.52)2(1−0.52)10−2+10C3(0.52)3(1−0.52)10−3+10C4(0.52)4(1−0.52)10−4 =1×1×0.00065+10×0.52×0.0014+45×0.2704×0.0028+120×0.141×0.0059+210×0.73×0.012231 =0.0065+0.0728+0.341+0.99828+1.875 ≈3.28773 Thus, the probability that fewer than 4 of them use their smartphones in meetings or classes is 3.28773

Assume that when adults with smartphones are randomly selected, 52% use them in meetings or classes. If 10 adult smartphone users are randomly selected, find the probability that fewer than 5 of them use their smartphones in meetings or classes.

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