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.

2021-12-15 Answered
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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Answers (1)

nick1337
Answered 2022-02-14 Author has 510 answers

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(1p)nx
Step 2
Required probability is obtained as follows:
P(X<5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
=10C0(0.52)0(10.52)100+10C1(0.52)1(10.52)101+10C2(0.52)2(10.52)102+10C3(0.52)3(10.52)103+10C4(0.52)4(10.52)104
=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

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