Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.

floymdiT 2020-10-21 Answered
Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.

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Expert Answer

Neelam Wainwright
Answered 2020-10-22 Author has 15951 answers

Given:
\(p=54\%=0.54\)
\(n=8\)
Definiton binomial probability:
\(\displaystyle{P}{\left({X}={x}\right)}=\frac{{{n}!}}{{{x}!{\left({n}-{x}\right)}!}}\cdot{p}^{{x}}\cdot{\left({1}-{p}\right)}^{{{n}-{x}}}\)
Complement rule:
\(\displaystyle{P}{\left(\neg{A}\right)}={1}-{P}{\left({A}\right)}\)
Addition rule for disjoint or mutually exclusive events:
\(P(A or B)=P(A)+P(B)\)
Evaluate the definition of binomial probability at \(x=6\):
\(\displaystyle{P}{\left({X}={6}\right)}=\frac{{{8}!}}{{{6}!{\left({8}-{6}\right)}!}}\cdot{0.54}^{{6}}\cdot{\left({1}-{0.54}\right)}^{{{8}-{6}}}={28}\cdot{0.54}^{{6}}\cdot{0.46}^{{2}}\approx{0.1469}\)
Result 0.1469

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