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Assume that when adults with smartphones are randomly​ selected, 53​% use them in meetings or classes. If 7 adult smartphone users are randomly​ selected, find the probability that exactly 5 of them use their smartphones in meetings or classes.

User Sammaye
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1 Answer

3 votes

Answer:


P(X=5)=(7C5)(0.53)^5 (1-0.53)^(7-5)=0.194

Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194

Explanation:

Let X the random variable of interest "number of adults with smartphones", on this case we now that:


X \sim Binom(n=7, p=0.53)

The probability mass function for the Binomial distribution is given as:


P(X)=(nCx)(p)^x (1-p)^(n-x)

Where (nCx) means combinatory and it's given by this formula:


nCx=(n!)/((n-x)! x!)

And we want to find this probability:


P(X=5)

Using the probability mass function we got:


P(X=5)=(7C5)(0.53)^5 (1-0.53)^(7-5)=0.194

Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194

User Ivan Drinchev
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